Gemara

(Mishnah -R. Akiva says, the bread is Me'akev the (two) lambs (Zivchei Shalmei Tzibur brought with Shtei ha'Lechem). These lambs are not Me'akev the bread;

R. Shimon ben Nanas says, these lambs are Me'akev the bread. The bread is not Me'akev them:

100b (Mishnah): The baking (of Shtei ha'Lechem and Lechem ha'Panim) is not Docheh Shabbos or Yom Tov;

(Ravina): One opinion forbids offering Nedarim and Nedavos (voluntary Korbanos) on Yom Tov. Do not say that this is only mid'Rabanan, lest people delay bringing them until Yom Tov. Rather, it is forbidden mid'Oraisa, like baking Shtei ha'Lechem is not Docheh Yom Tov. This is not a decree lest one delay baking them!

Shabbos 133a (Beraisa): Milah overrides Yom Tov only in its time.

(Rava): "Hu (Levado Ye'aseh Lachem)" - (Melachah is permitted on Yom Tov only for Ochel Nefesh, i.e. preparation of food, but) not Machshirav (things used for Ochel Nefesh, e.g. to build an oven). "Levado" - Milah in its time is Docheh Yom Tov, but not Milah after its time. A Kal va'Chomer teaches this.

(Mishnah - R. Akiva): The general rule is, needs of Milah override Shabbos only if they cannot be done before Shabbos.

(Mishnah): If one did not grind the cumin before Shabbos, he chews it with his teeth and puts it on. If he did not mix wine and oil (this was used to heal) before Shabbos, each is put by itself;

134a (Beraisa): Things that may not be done for Milah on Shabbos may be done on Yom Tov, i.e. grinding cumin and mixing wine and oil.

Question (Abaye): Presumably, one may grind cumin on Yom Tov because it could be added to (spice) food. Also wine and oil are proper on Shabbos for a Choleh (who is mildly sick)!

(Beraisa): One may not mix wine and oil for a Choleh on Shabbos;

R. Shimon ben Elazar says that R. Meir permits. (Presumably, our Stam Mishnah is like R. Meir.)

Answer: They are not mixed thoroughly for a Choleh. They must be mixed thoroughly for Milah.

Question: We should be allowed to mix them like for a Choleh!

Answer: Indeed, even though the Mishnah says 'he puts the wine on by itself and the oil on by itself', it permits this! (Since they are not mixed well, almost all the oil will be on top. It is like putting them on separately.)

Megilah 7b (Mishnah): The only difference (regarding Melachah) between Shabbos and Yom Tov is Ochel Nefesh.

This implies that they are the same regarding Machshirim. This is unlike R. Yehudah;

(Beraisa): The only difference between Shabbos and Yom Tov is Ochel Nefesh;

R. Yehudah permits Machshirei Ochel Nefesh.

Yerushalmi Pesachim (6:3) - Question: R. Akiva permits Machshirim that could not be done before Shabbos. If a wart arose on Shabbos, or the Mizbe'ach fell on Shabbos, will he say that we may cut it or fix on Shabbos?!

Answer: The Min of warts could be cut from before Shabbos.

Question: If one was Tamei Mes, and his seventh day was on Erev Pesach on Shabbos, he may not have his second Haza'ah (sprinkling with Mei Chatas) that day to enable him to offer Korban Pesach!

Answer: The Min of Haza'ah can be done the day before.

Rishonim

Rambam (Hilchos Milah 2:10): Machshirei Milah are not Docheh Yom Tov, even if it is the eighth day, since they can be done from before Yom Tov. We learn from a Kal va'Chomer. Machshirei Milah are not Docheh Shevus, i.e. mid'Rabanan stringencies of Shabbos. Surely they are not Docheh a Lav in the Torah!

Kesef Mishneh: Rashi explains that a Kal va'Chomer from Tzara'as would have permitted Milah not in its time, so Rava needed to teach that it does not. The Rambam discusses Machshirei Milah through a proper Melachah. Since one may not do Machshirim through Melachah, one may not do them through Shevus. Chachamim did not distinguish. The Kal va'Chomer is based on the Rambam's reasoning. Or, perhaps he holds that Rava meant that a Kal va'Chomer forbids Machshirim.

Kiryat Sefer: Milah is Docheh the Lav and Aseh of Yom Tov only if at the time he fulfills the Mitzvah. One does not fulfill the Mitzvah while doing Machshirim.

Ramban (Shabbos 124b DH Nimtzeis and DH v'Kasheh): We do not say Mitoch (since Melachah is permitted on Yom Tov for Ochel Nefesh, it is permitted for other needs) regarding Machshirim. E.g. one may not extinguish a lamp (to permit relations), or Machshirim of Milah in its time, Lulav or Shofar. Regarding Shabbos, carrying a baby in Reshus ha'Rabim (for the sake of Milah) is called Machshirim. If so, it should be forbidden on Yom Tov! Why is this different than taking an animal to a Shcohet, which is permitted? Regarding food, moving the food is considered (Meleches) Ochel Nefesh itself (and not merely Machshirim), for it says "Asher Yochal l'Chol Nefesh Ye'aseh Lachem." Similarly (Hagahas Rav I.Z. Meltzar - therefore,) Beis Hillel permit also every need (that is not food), due to Mitoch. On Shabbos, Milah itself is Docheh Shabbos, but not bringing the baby or anything that could be done before Shabbos. This shows that for Ochel Nefesh itself, Machshirim is the only case in which something is forbidden because it could have been done the day before, i.e. according to R. Yehudah.

Or Some'ach: R. Nisim Ga'on (Shabbos 24b) explains that the Kal va'Chomer that would permit Milah not in its time is that Ochel Nefesh needed for Yom Tov is Docheh Yom Tov, even though covenants were not made about this. (All the more so Milah is Docheh Yom Tov!) Rishonim challenged this, because Ochel Nefesh is a Mitzvah that will pass (if not done in its time). This does not apply to Machshirim of Milah in its time (since they could be done beforehand)! We can make a Kal va'Chomer as follows. Ochel Nefesh is not Docheh Shabbos, but Machshirei Ochel Nefesh are Docheh Yom Tov. Milah in its time is Docheh Shabbos, all the more so its Machshirim are Docheh Yom Tov if they could not be done from before Yom Tov! Even though the Min (category) of Machshirim can be done the day before, therefore, they are not Docheh Shabbos, but they are Docheh Yom Tov when they could not be done before Yom Tov. The Beraisa that forbids is like Rabanan, who forbid Machshirei Ochel Nefesh on Yom Tov, so there is no Kal va'Chomer. Perhaps R. Yehudah would permit Machshirei Milah on Yom Tov. Surely, the Halachah is that it is forbidden, just like Haza'ah (sprinkling with Mei Chatas) is forbidden on Shabbos even for the sake of Korban Pesach. It was clear to the Yerushalmi that one may not cut off a wart that arose on Shabbos, or fix the Mizbe'ach if it fell on Shabbos, for the Min of such Machshirim can be done from before Shabbos.

Or Some'ach (DH Emnam): A Beraisa says that there was an enactment for Milah (to allow people who left their Techum to move 2000 Amos in every direction). The Yerushalmi says that it is like R. Eliezer, who permits Melachos to make a knife for Milah on Shabbos. I.e. only he would permit leaving the Techum for Milah. If R. Yehudah permits Machshirei Milah on Yom Tov, the Beraisa could be like him! Rather, all forbid Machshirei Milah on Yom Tov just like on Shabbos. There is another proof is from the Yerushalmi, which challenged R. Akiva from when the Mizbe'ach fell on Shabbos. It held that just like Avodah is Docheh Shabbos, also Machshirei Avodah. It answered that the kinds of Machshirim that can (sometimes) be done beforehand are not Docheh Shabbos. If so, according to R. Yehudah, Machshirei Tamid should be Docheh Yom Tov! The day that a Tzeduki poured the water for Nisuch ha'Mayim on his feet, people stoned him with their Esrogim, and the Mizbe'ach became dented. They did not fix it. Why wasn't it permitted for the sake of the afternoon Tamid? It became dented on Yom Tov! R. Yehudah permits fixing a roasting spit on Yom Tov! It is difficult to say that it was Shabbos, when we take the Esrog in the Mikdash (and this is why Machshirei Avodah were forbidden).

Or Some'ach: It seems that the Isur of Machshirim is mid'Oraisa. The baking of Shtei ha'Lechem is not Docheh Yom Tov, even though there is a Kal va'Chomer. Machshirei Ochel Nefesh are Docheh Yom Tov, all the more so Machshirei Shtei ha'Lechem should be Docheh Yom Tov! Do not say that it is only mid'Rabanan that they are not, for Ravina learned from this that the Torah forbids Nedarim and Nedavos on Yom Tov. We hold like R. Yehudah. Will we say that the Halachah does not follow the Stam Mishnah?!

Note: The Stam Mishnah in Megilah is unlike R. Yehudah!

Or Some'ach (ibid.): Seemingly, this is wrong. No Melachah for Shtei ha'Lechem is Docheh Shabbos! However, we can learn from Lechem ha'Panim, which is not Docheh Yom Tov. Also, the Rambam rules like the opinion that Shtei ha'Lechem is Me'akev the lambs. If so, they are Machshirim for the lambs, which are Docheh Shabbos. Baking Shtei ha'Lechem is like fixing a spit! Even so, it is not Docheh Yom Tov. This proves that mid'Oraisa it is not Docheh. Also baking Lechem ha'Panim is not Docheh Yom Tov, even though their Avodah includes burning the spoons of frankincense that accompany them, which is Docheh Shabbos. This proves that all agree that mid'Oraisa, Machshirei Milah are not Docheh Yom Tov (except for R. Eliezer, who permits even on Shabbos - PF). I explain that Ochel Nefesh is Docheh Yom Tov because the Mitzvah pertains to Yom Tov, i.e. to have Simchah on Yom Tov. Therefore, even Machshirei Ochel Nefesh are Docheh Yom Tov. Ochel Nefesh is not Docheh Shabbos, for there is no Mitzvah of Simchah on Shabbos (just a Mitzvah of Oneg, from Nevi'im). Milah is not connected to Yom Tov. It is Docheh Yom Tov just like it is Docheh Shabbos, therefore, its Machshirim are not Docheh. Ochel Nefesh is not merely Docheh Yom Tov; it was never forbidden.