Implied question: He did not say [that the Halachah follows the Machri'a only] in our Mishnah!

Answer: It connotes like this, that the Halachah does not follow him, because our Stam Mishnah is unlike him.

Explanation #1: Hachra'ah is like leniencies of rags (29b). R. Eliezer and R. Yehoshua explicitly mentioned in their words Muchan and not Muchan, i.e. he hung on a peg or left it in back of the door;

They revealed in their words that there is reason to distinguish between them, just they hold that we do not distinguish. Therefore, R. Akiva, who distinguishes between them, is Machri'a.

Similarly, R. Yehudah is Machri'a, for R. Shimon and R. Meir mentioned in their words hot and cold [water].

Distinction: A "third Hachra'ah", which is not a Hachra'ah (the Halachah does not necessarily follow it) is like in Pesachim (21a) - a barrel of Terumah wine that became Tamei. Beis Shamai says, we spill it out. Beis Hillel says, we sprinkle [in the house for a nice smell;

R. Yishmael b'Rebbi Yosi says, I will be Machri'a. [If it became Tamei] in the field, we spill it all out. In the house, we sprinkle it;

They said to him, a third Hachra'ah is not a Hachra'ah, for Beis Shamai and Beis Hillel did not mention in their words a house and field. They did not reveal that there is a reason to distinguish between a house and a field. This is considered a third Hachra'ah.

This is unlike Rashi, who explained there that Beis Shamai's reason is not due to pitfall (lest someone come to eat it), rather, for another reason, e.g. smell (one may not benefit from the smell of Tamei Terumah). Rather, it is because they did not mention in their words a house and field, like I explained.

Implied question: It could have said that a Talmid's Hachra'ah is not a Hachra'ah, like it says here!

Answer: It says a bigger Chidush. Even if [R. Yishmael b'Rebbi Yosi] were not a Talmid, it is not a Hachra'ah.

Implied question: A Mishnah in Bechoros (43b) teaches that Beis Shamai say, one blesses on oil, and afterwards on myrtle. Beis Hillel say, one blesses on myrtle, and afterwards on oil;

R. Gamliel says, I will be Machri'a. We merit [benefit from] the smell of oil, and anointing it. We merit the smell of myrtle, but not anointing it. R. Yochanan said, the Halachah follows the Machri'a!

R. Tam explained that this is like Hachra'ah in the entire Gemara.

Rebuttal: This is wrong. Hachra'ah is only like I explained. There, he merely explains Beis Shamai's reason.

Explanation #2 (R. Chananel): A third Hachra'ah is not a Hachra'ah, i.e. of a third generation, like R. Yishmael b'Rebbi Yosi, who was the third generation from Beis Shamai and Beis Hillel;

Implied question: Third generation is not precise. The same applies to a second generation!

Answer: In any case it mentioned Hachra'ah of a third generation due to the Beraisa in Pesachim (which discusses Hachra'ah of a third generation).

Explanation: This is only to bathe, but one may enter to be Mezi'a even on Shabbos, just like on Yom Tov, like it says below that even on Shabbos Zei'ah was permitted until the decree;

After the decree, they forbade even on Yom Tov, for regarding Yom Tov it was taught "after many transgressed, they began to forbid."

Implied question: [The Tana] could have taught them together! If they plugged up the holes of a bathhouse from before Shabbos or before Yom Tov, the next day he may enter and be Mezi'a, and on Motza'ei Shabbos or Motza'ei Yom Tov he may bathe immediately!

Answer: If he taught them together, one might have thought that only on Shabbos they forbade Zei'ah, but not on Yom Tov, for the episode brought was on Shabbos;

Therefore, he taught them separately. Now, "after many transgressed" refers to Yom Tov, but not to Shabbos, for Zei'ah was not mentioned regarding Shabbos. (It was never forbidden on Shabbos and permitted on Yom Tov.)

Explanation #1 (Rashi): They did not need to be concerned lest the water [with which they showered] was heated on Shabbos from the heat of the bathhouse.

Question: This connotes that he holds that they rinsed in hot water that was heated from before Shabbos. Above, R. Yehudah himself forbade!

Answer: Perhaps he distinguishes between Shabbos and Yom Tov.

Explanation #2: The text of the Tosefta (3:3) says "they rinsed in cold water, but its hot water was covered." This was lest everyone think that they bathed in hot water.

Implied question: In our entire Sugya and in our Mishnah about a kettle cleared [from a fire], it connotes that warming water for the need of drinking is permitted, for warming it is not cooking it. Here we forbid!

Answer (Riva): This resembles bathing in hot water, and he will come to heat water to bathe his body.

Explanation #1: [One may not bring the kettle] as long as the towel is there, lest water fall on the towel and he come to squeeze.

Explanation #2: One may not bring [the kettle] due to healing. They decreed due to grinding ingredients [to make medicine] more than regarding a towel, which does not look so much like Refu'ah.

Question: Why is a Kli Sheni different than a Kli Rishon? If it is Yad Soledes Bo (so hot that if one touches it, he removes his hand), even a Kli Sheni [can cook]!

If it is not Yad Soledes Bo, even a Kli Rishon cannot cook!

Answer: A Kli Rishon, since it stands on the fire, its walls are hot, and it retains its heat a long time. Therefore, Chachamim gave a Shi'ur that as long as it is Yad Soledes Bo, it is forbidden;

A Kli Sheni, even if it is Yad Soledes Bo, is permitted, for its walls are not hot. It cools off.

Implied question: [Even if he did not speak in Leshon ha'Kodesh,] one may not think [about Torah] in the bathhouse!

Answer: We can say that the Isur to think [about Torah in the bathhouse] is only in Leshon ha'Kodesh, and he thought in Leshon Chol. (Rashash - the Rashba says that language does not apply to thought. Sha'agas Aryeh (7) points out that Tosfos disagrees.)