Gemara

(R. Avahu citing R. Yochanan): Heter joins to Isur (to comprise a Shi'ur (quantity) to be liable) only regarding Isurei Nazir, for the Torah said "Mishras". (A Nazir is liable for eating bread that absorbed wine.)

(Ze'iri): Also regarding the Isur of Haktaras (burning on the Mizbe'ach) Chametz, Heter joins to Isur!

This is like R. Eliezer, who expounds "Kol (Se'or... Lo Saktiru)". He holds that Heter joins to Isur also regarding Chametz during Pesach! Ze'iri taught about Haktarah to teach that it has a Shi'ur.

Question (Abaye - Mishnah): If a Chulin porridge contained Terumah garlic and oil, and a Tevul Yom (one who immersed from Tum'ah today. He is Metamei Terumah, but not Chulin.)

(R. Yochanan): This is because a non-Kohen is lashed for eating a k'Zayis.

One is liable for a k'Zayis of the mixture, for the Chulin joins to the Terumah!

Answer (Rav Dimi): No. A non-Kohen is lashed for eating a k'Zayis (of Terumah) bi'Chdei Achilas Pras (within the time to eat a half loaf, i.e. three or four eggs).

37a - Question (Abaye): Why may we learn from "Mishras" that Heter joins with Isur? Perhaps it forbids only Ta'am k'Ikar (a food that absorbed the taste of Isur)!

(Beraisa): "Mishras" forbids Ta'am k'Ikar. A Nazir is liable for drinking water that absorbed taste from grapes. We learn from here to all Isurim.

Answer: R. Avahu said that R. Akiva learns from "Mishras" that Heter joins with Isur. (The Tana of this Beraisa disagrees.)

(Beraisa - R. Akiva): If a Nazir soaked his bread in wine and ate a k'Zayis of bread and wine, he is liable.

Question (Rav Ashi - Beraisa): "Mi'Kol Asher Ye'aseh mi'Gefen ha'Yayin..." teaches that all Isurim (of vine products) of Nazir join with each other.

If Heter joins to Isur, there is no need to teach that Isur joins to Isur!

Answer (Rav Kahana): Heter joins to Isur only if they are eaten together. Isur joins to Isur even if they are eaten one after the other.

Pesachim 42a (Mishnah): One transgresses for the following during Pesach: Kutach of Bavel (a dip made with bread), beer of Madai (which has barley)...

43a (Rav Nachman): Our Tana is like R. Eliezer:

(Beraisa - R. Eliezer): One who eats proper Chametz of grain is Chayav Kares. One who eats a mixture of it transgresses a Lav;

Chachamim say, one who eats a mixture does not transgress anything.

44a - Question (Abaye, against Rav Dimi): If the Torah forbids a k'Zayis bi'Chdei Achilas Pras, why do Chachamim exempt one who eats Kutach on Pesach?

Answer (Rav Dimi): Kutach is different. One does not normally eat a k'Zayis (of Chametz) bi'Chdei Achilas Pras.

45a (Rav Ashi): R. Akiva holds that Heter joins to Isur regarding Isurei Nazir and absorptions of a Korban Chatas. Shenei Kesuvim (two verses, one of which could have been learned from the other) do not teach about other cases.

Chachamim hold that Chatas teaches that Heter joins to Isur. We cannot learn Chulin from Kodshim. Mishras teaches that Ta'am k'Ikar. We learn to all Isurim.

Rishonim

Rif (Pesachim 13a): Chachamim say that one who eats a mixture does not transgress anything, i.e. he is not lashed. They agree that it is forbidden. If there is k'Zayis bi'Chdei Achilas Pras, Chachamim agree that he is lashed.

Rebuttal (Ba'al ha'Ma'or): The Rif rules like Chachamim. Really, the Halachah follows R. Eliezer. Our Stam Mishnah is like him. There is a stringency to Heter Mitztaref l'Isur over Ta'am k'Ikar. Ta'am k'Ikar is only when a k'Zayis of Isur dissolved and can be tasted and one eats a k'Zayis of Isur within Kdei Achilas Pras. It is forbidden in the entire Torah, but one is lashed only regarding Isurei Nazir. Heter Mitztaref l'Isur applies even when the Isur cannot be tasted, and one eats a k'Zayis in all, half Isur and half Heter.

Defense (Milchamos Hash-m): The Halachah does not follow R. Eliezer. He learns from Chametz that Heter Mitztaref l'Isur for all Isurim. We hold that Heter joins only if there is k'Zayis bi'Chdei Achilas Pras. R. Yochanan taught that the Halachah follows a Stam Mishnah. The Gemara did not ask why he rules against it! We follow the Amora'im.

Question: Rav Nachman said that the Mishnah in Pesachim is like R. Eliezer, who says that Heter joins to Isur also regarding Chametz. Why does the Mishnah discuss only mixtures in which the Chametz can be tasted?

Answer #1 (Ba'al ha'Ma'or): In every case in the Mishnah, the Chametz helps give the mixture a new taste. One does not taste (proper) Chametz. This is why the Gemara says that Heter Mitztaref l'Isur, and not Ta'am k'Ikar.

Rebuttal (and Answer #2 - Hasagos ha'Ra'avad): The Gemara did not say that R. Eliezer holds that Heter Mitztaref l'Isur regarding the Mishnah. The Mishnah discusses Ta'am k'Ikar! Rather, he holds that Heter Mitztaref l'Isur even regarding Chametz and Matzah, which do not give taste to each other. We concluded that there is not a k'Zayis of Chametz bi'Chdei Achilas Pras of Kutach. Nevertheless, it is forbidden mid'Oraisa, but one is not lashed for it.

Rambam (Hilchos Nezirus 5:4): Heter does not join to an Isur regarding Nazir. If wine mixed with honey, or raisins were pressed with figs, and it all tastes like wine or raisins, he is lashed only if there was a k'Zayis of Isur within three eggs of the mixture, and he ate three eggs. This is like Isurim that apply to everyone.

Kesef Mishneh: Abaye tried to prove from a Beraisa that Heter Mitztaref l'Isur also for other Isurim, e.g. Terumah. Rav Dimi answered that R. Yochanan taught that R. Akiva holds that only Isurei Nazir join with Heter when there is not a k'Zayis of Isur bi'Chdei Achilas Pras. According to Rabanan, all Isurim join with Heter only when there is a k'Zayis of Isur bi'Chdei Achilas Pras.

Kesef Mishneh (Chametz u'Matzah 1:6 DH v'Kodem): Why did the Rambam rule unlike R. Yochanan? No one argues with him! It seems that this is because R. Yochanan's law is like R. Akiva, but he himself holds like Chachamim. Chachamim hold that Heter Mitztaref l'Isur regarding Chatas, but we cannot learn Chulin from Kodshim. This connotes that we do learn all Kodshim! The Rambam rules like the Gemara in Nazir, that Chatas and Nazir are both needed for Ta'am k'Ikar.

Rambam (Hilchos Chametz u'Matzah 1:6): One is Chayav Kares only for eating Chametz itself. For a mixture, such as Kutach in which Chametz is mixed, one is lashed and there is no Kares, for it says "Kol Machmetzes Lo Sochelu." If he ate a k'Zayis of Chametz within three eggs he is lashed mid'Oraisa.

Kesef Mishneh (DH v'Lachen): It seems that the Rambam rules like R. Eliezer. However, if so Heter Mitztaref l'Isur, and he should obligate Kares even for a k'Zayis of Kutach! Perhaps Heter joins only when the majority is Isur. However, the Rambam (Nezirus 5:4) says so even when the majority is Heter! The Gemara in Nazir says that Ein Heter Mitztaref l'Isur when the majority is Heter. Perhaps this was not in the Rambam's text. The Rashba connotes that it is an addition from the Ge'onim.