Before us is Mishnah 11 in the second chapter of Maseches Orlah. Its central topic is the law of 'zeh v'zeh gorem': when a forbidden substance and a permitted one combine and together produce a single effect, is the result permitted or forbidden? The Tannaim in our Mishnah disagree about this question.
The text of the Mishnah:
"Se'or shel chullin v'shel Terumah shenaflu l'toch isah, lo b'zeh k'dei l'chametz v'lo b'zeh k'dei l'chametz, v'tzirfu v'chimtzu" - two types of leavening agent fell into a single batch of dough: one of chullin and one of Terumah. Neither of them on its own had enough potency to leaven the dough, but when they combined together there was enough to leaven it.
The view of Rabbi Eliezer:
Rabbi Eliezer says "Achar ha'acharon ani ba" - we follow the leavening agent that fell in last:
If the Terumah leaven fell in last, the dough is considered Terumah and is forbidden to anyone who is not a kohen.
If the chullin leaven fell in last, the dough is permitted.
The Gemara in Pesachim qualifies this:
The Gemara in Pesachim qualifies Rabbi Eliezer's words: his ruling that the dough is permitted when the chullin fell in second was stated specifically in a case where the Terumah leaven was removed from the dough before the chullin leaven fell in, so that only the results and influence of the Terumah leaven remained, and not the leaven itself. Under these circumstances the dough is permitted, because the forbidden leaven is no longer present.
But if the Terumah leaven is still in the dough, there is a problem, since Rabbi Eliezer holds that 'zeh v'zeh gorem' is forbidden: the combining of the potency of the Terumah leaven with the potency of the chullin leaven renders the dough forbidden. It emerges that the leniency in the case where the chullin fell in last stems entirely from the fact that the Terumah leaven is no longer there, and nothing remains of it but its taste and its influence.
The view of the Chachamim:
"V'chachamim omrim: bein shenafal issur batechilah bein basof, l'olam eino oser ad sheyehei bo k'dei l'chametz" - according to the Chachamim it makes no difference whether the forbidden substance, the Terumah leaven, fell in first or second. The dough becomes forbidden only if the Terumah leaven on its own has the potency to leaven. If it can leaven by its own power alone, the dough is forbidden, and if not, it is permitted.
The words of the Chachamim were stated even where the Terumah leaven is still present in the dough, since in their view 'zeh v'zeh gorem' is permitted: when two different agents combine together to leaven, the result is permitted. There is a prohibition only when the forbidden substance is capable of bringing about the leavening by its own power.
In summary: in this Mishnah the Tannaim disagree about the law of 'zeh v'zeh gorem'. Rabbi Eliezer says "Achar ha'acharon ani ba", and in his view 'zeh v'zeh gorem' is forbidden, and therefore the dough is permitted only when the Terumah leaven was removed and nothing remains but its effects. The Chachamim hold that 'zeh v'zeh gorem' is permitted, and in their view the dough does not become forbidden, whether the forbidden substance fell in first or last, unless the Terumah leaven on its own has enough potency to leaven.