Sanhedrin 63. See in the top Tosphot the part where Rabbainu Tam explains this Gemara.

The question I am dealing with here is that R. Ami says one does the three inner services in one span of forgetting is liable one sin offering. This seems to be fine even with people that disagree with it. But Rabbi Zakai said one who does all four services is liable one sin offering and this seems to get everyone especially R Yochanan upset. What is the difference?
We have one verse to put the three services together "Don't serve idols." Another verse which van be used to separate the services "Don't bow to idols."
To Rabbi Ami it seems "bowing" is coming to teach on itself [doing it with the other three means one would have to bring two sin offerings.] And R Yochanan seems to be OK with this. But why?

 If it is teaching about itself alone, then it is not teaching about the whole category of "service." You can say two things here. You can say what would it have taught us if it could? To divide. But it can't do that because of "Dont serve" so all that is left for it to do is to  divide itself from the others.

Another thing you could say is that it tells us to divide service according to its way from the others.

Now let's look at R. Zakai. "Don't serve" includes all kinds of service--inner and outer. But then why does "bowing" get mentioned separately? To tell us it is a mere prohibition. That is he thinks that since there is nothing it can tell us about the whole category of service it can only tell us about itself. This made R.Yochanan upset. If used to divide itself --that would be OK. But to be used to tell us it is a mere prohibition that is not OK. What is the difference?
One we say is teaching about the whole category and the other we say is not. The later is true. But the first claim? Perhaps that is the difference. R Zakei thinks bowing to divide only teaches about itself so it is equal to what he says. R Ami says it teaches about service according to its way and so can be considered to be teaching about the whole category.

 סנהדרין סג. תוספות בראש הדף. ר. אמי אמר שמי שזיבח קיטר וניסך בהעלם אחד חייב אחת. אביי פירש שטעמו בא מן הפסוק "לא תעבדם". הכתוב עשה כולן עבודה אחת. בדף סב. רבי זכי אמר אותו דבר אלא שהוסיף השתטחות. רבינו תם אמר שמילת השתטחות מופיע במשפטו של רבי זכי לא במשפטו של רבי אמי. הסיבה לכך היא שיש פסוק בעשרת הדברות "לא תשתחווה להם ולא תעבדם."  הפסוק אסר כל מין עבודה  והוציא השתטחות להיזכר בפני עצמה. ולכן כל עבודות פנימיות נחשבות עבודה אחת, והשתטחות נחשבת בפני עצמה ואם עשה כולן בהעלם אחד חייב שתיים. אחת בשביל השלש, ואחת בשביל השתטחות. ועכשיו למה ר' יוחנן אמר לר' זכאי "פוק תני לברא" שיש סברה לומר שלשת עבודות הפנימיות נחשבות אחת אבל לא השתטחות. למה? אם השתחוויה בא ללמד על עצמה, אם כן אינו בא ללמד על הכלל כולו. אפשר לומר פה שני דברים. אפשר לומר אם היתה באה ללמד על הכלל כולו מה היתה מלמדת? לחלק. אבל אינה יכולה לעשות את זה בגלל לא תעבדם עשה כולן עבודה אחת. ולכן כל מה שנשאר הוא לחלק על עצמה. דבר שני שאפשר לומר הוא שהיא באה גם לחלק עבודה כדרכה.עכשיו נסתכל ברבי זכאי. לפי ר' תם שיטתו היא שהשתחווייה ללאו יצאה. זאת אומרת שהיתה בכלל לא תעבדם ויצאה מן הכלל. אי אפשר שהיא תלמד מה שהוא על הכלל כולו בגלל שלא נשאר מה ללמוד. כבר לא תעבדם עשה כולן עבודה אחת. ר' יוחנן אינו מסכים עם זה. זאת אומרת שאם השתחווייה היתה באה ללמד על עצמה זה בסדר, אבל אם היא באה לאו גרידה לא. מה החילוק?אם היא באה ללאו ברור שהיא לא מלמדת על הכלל כולו. אבל אם היא באה לחלק למה כן? אפשר לומר החילוק הוא זה. רבי זכאי סובר שאם השתטחות באה לחלק זב גם נחשב להיות שהיא מלמדת רק על עצמה. ולכן יש לו ברירה לומר באיזה אופן היא באה ללמד על עצמה. אבל ר' אמי סובר שהשתטחות באה גם ללמד על עבודה כדרכה, ולכן אפשר שהיא נחשבת להיות מלמדת על הכלל כולו.

. Rabbi Yochanan told  Rabbi Zackai "go teach it on the street". It seems the reason is Zakai said something stupid. But what he said wrong seems to be a mystery. The one version has it he said "one who does all four services (sacrifice, burning, pouring , bowing) to an idol brings one sin offering."
Then Rabbi Ami says one who does the major three services (sacrifice, burning, pouring) to an idol brings a sin offering.
Rashi says the original statement of R Zakai is the same as Rabbi Ami.
Rabbainu Tam says the original statement did have "bowing" in it. And this idea makes some sense because "Don't serve idols" would have put all three services into one, and "Don't bow" would have come to teach on itself [bowing] that it also is liable.


Let me first reiterate what Rabbainu Tam is saying. Rabbi Ami is fine. We have "Don't serve idols" to tell us the three inner services are all one.  And we have "Don't bow" to tell us bowing is also liable. That is fine. Then we have Rabbi Zakai saying if one does all four services he is liable once. And Rabbi Yochanan told him, "Teach it on the street". We know R. Zakai can't be saying like R. Ami because then of he would do all four he would be liable twice. [That is after all what comes out from R Ami.] So to R. Zakai, bowing has to be coming for a mere prohibition. And in essence that is fine. We have Rabbi Yose doing the same in Shabat with the verse "don't lite a fire on Shabat"
But this is where my learning partner noticed the crucial difference between Rabbi Yose and Rabbi Zakai.

Why was Rabbi Yose allowed to use fire for a mere prohibition? Don't we always have a principle, "Whatever was in a category and has come out of the category comes to teach about the whole category, not about itself alone." How did we deal with this problem in the case of Rabbi Yose? We said just one page back that since the acts of work on Shabbat are all separate anyway we have nothing we can do with fire so it has to be teaching about itself alone. This was fine with R Yose. But it can't work for Rabbi Zakai because he does not have the four services separated. To him they are all together, so he has no possible reason to use "bowing" for itself alone, and that is why Rabbi Yochanan  told him "Teach it on the street."

Now you could ask why did this question not bother Rabbi Yochanan when it comes to the law of R Ami? Simple. Rabbi Ami uses "Don't serve idols" to put all three services into one. And so bowing can't be used for the whole category. And so it can come out to teach about itself alone.

Tosphot definitely says that if Rabbi Zakai is using "bowing" for a mere prohibition, then he can't be using "service" to put all three services into one.
But that using "bowing" for itself would not have presented any problem in terms of using "service" to put all three together.

However this still needs hammering out. I am confused at this point about Rabbi Ami. Let me say what is bothering me. Is bowing in the category of service? If yes then why could it not be included in "Dont serve idols" and have that verse tell us all four are one category? And we could say it is mentioned separately because you might not have known it is a service. If it is not in the category of service then the whole question does not even start. Stay tuned.

Next Day:
I suggested today to my learning partner a problem with his idea of how to explain Tosphot. My idea is this: Is bowing in the category of service? Probably according to how we have been treating it up until now. That means it is in "don't serve idols." So since don't serve means to make all the services in the sense of the verse into one service that includes bowing. So now we have just what Rabbi Zakai wants--for all four serves to be counted as one. And then why is bowing mentioned separately? to tell us it is a mere prohibition.  So Rabbi Zakai makes perfect sense even according to the logic that we used to explain Rabbi Ami.
It is funny also the way Rabbainu Tam wants to explain Rabbi Ami --that "bowing" comes to teach that it is a separate prohibition. If it was in the category of "service" anyway it seems kind of arbitrary to pull out "bowing" just to add a prohibition.

I think it all depends on the direction of your logic. I think Rabbi Zakai started out thinking as the first step that we have bowing comes for a mere prohibition. then he asked what is serving for? And the answer is like Abyee said to put the other three into one category. And this makes perfect sense.
But we see Rabbi Yochanan did not like this and on page 62 also we see the Gemara wants to start out in Shabat that anything extra will come to divide. You have to look there to see this. It is only because we don't need fire to divide that we can use it for a mere prohibition. And this is how R Yochanan is thinking on pg 62 and 63. since even if we use "Don't serve" to put all three together we can still use "bowing" to come for its own prohibition. And that is what makes him think that Rabbi Zakai was not making sense.

April 12 it became clear to me what Tosphot is saying. There are only two "drashot." One is on "Don't serve" and the other is bowing comes to divide. Rabbi Yochanan said to Rabbi Zakai you don't hold from the later so you must hold from the former but if so then bowing comes to make its own prohibition  and so doing them all together would mean bring two sin offerings.

April 13 Today a landslide of questions on Tosphot fell on me. Mainly there are two major branches. One thing is this: R Ami is thinking what? That don't serve puts all three together so dont bow must come out to teach on the whole category. Since it can't teach on those three it teaches on what is left and that is itself. But there is one thing left and that is service according to its way.  So maybe that is what R Ami means. But R Zachai might disagree with that and say teaching on itself is not called teaching on the whole category. And just arbitrarily adding service according it it way is just ad hoc. That leaves him free to use bowing for a mere prohibition. But what is difficult here is the question where they place service according to its way. I am not sure if this is a question but it is a point my learning partner brought up.

The other area of question here is "Why can't R Zachai simply look at the explanation of Abyee 'service comes to comes to put all services together' and say that 'bowing' is included?"