Gemara

(Mishnah - Sumchus): A Yisrael must be Me'arev with Chulin.

Inference: Sumchus argues only here, but he agrees that a Nazir can be Me'arev with wine. He could regret his vow of Nezirus and ask a Chacham to annul it.

Question: If so, he should also permit a Yisrael to be Me'arev with Terumah. He could annul making it Terumah!

Retraction: Rather, Sumchus holds like Chachamim, who forbid Shevus (mid'Rabanan Isurim of Shabbos, e.g. separating Terumah) Bein ha'Shemashos.

32b (Mishnah): If an Eruv was in a tree above 10 Tefachim, it is invalid;

If it is below 10 Tefachim, it is valid;

The tree is in Reshus ha'Rabim. He intended his Shevisah to be on the ground. The Isur to use a tree is mid'Rabanan. Our Mishnah is Rebbi, who permits Shevus during Bein ha'Shemashos.

34b (Mishnah): If one was Me'arev in a cabinet and lost the key, even so it is valid;

R. Eliezer says, if he does not know where the key is, it is invalid.

35a (Abaye and Rava): The case is, the lock is tied with ropes, and a knife is needed to break them. The first Tana holds like R. Yosi, who permits moving [almost all] Kelim on Shabbos;

R. Eliezer holds like R. Nechemyah, who permits moving a Kli only for its intended purpose. (A knife is not made for cutting rope.)

Kidushin 81b: Rav Acha bar Aba visited Rav Chisda (his son-in-law). Rav Acha put his granddaughter in his lap.

Rav Chisda: She is Mekudeshes! [And even if not,] Shmuel taught that we do not use a woman!

Rav Acha: Shmuel permits what is done l'Shem Shamayim (e.g. to show my daughter that I cherish her daughter).

Rishonim

Tosfos Rid (81b DH Amar): Rashi explains that Rav Chisda rebuked Rav Acha, for one must distance from an Eshes Ish. Why is this more stringent than the Isur of one's granddaughter? Rather, since she is Mekudeshes, she is like an adult, and one may not treat her like a minor and put her in his lap.

Bartenura (Eruvin 3:3): Cutting rope is Shevus. R. Eliezer permits moving a Kli only for its intended purpose. Since one must transgress two Shevusim in order to get the Eruv, even Rebbi forbids Bein ha'Shemashos.

R. Akiva Eiger (1:159 DH v'Nir'eh): Seemingly, 32a refutes the Bartenura! An Eruv in a tree below 10 is Kosher, even though to get it he must transfer from Karmelis (the tree) to Reshus ha'Rabim, and use a tree! Even ha'Ozer asked this, and answered that there, the two Shevusim do not come at once. The moment he takes it from the tree, he did not yet rest it in Reshus ha'Rabim. When he rests it in Reshus ha'Rabim, he is no longer using the tree. When he opens the cabinet, both Shevusim come together -- destroying the Ohel, and using a knife not for its normal use. We can say that two Shevusim that come together are more stringent, and are forbidden even in the Mikdash.

Tosfos (30b DH Ela): If Sumchus forbids Shevus Bein ha'Shemashos, why may a Nazir be Me'arev with wine? He may not permit his vow Bein ha'Shemashos! For the needs of Shabbos, e.g. to be able to drink wine, it is permitted.

Hagahos Mordechai (Shabbos 472, p.156, middle of column 1, before 17b): We permit putting hot metal into the Mikveh due to the pain of the Kohen Gadol (Yoma 34b), even though this extinguishes a metal coal.

Poskim

R. Akiva Eiger (ibid.): R. Yehudah (Yoma 13b) holds that the Kohen Gadol marries a second wife, and divorces both wives on Tanai before Yom Kipur. Sha'agas Aryeh (93) asked why he must marry and divorce? He could divorce his wife and be Mekadesh a second girl, both on Tanai "if I will enter the Beis ha'Keneses"! (He will enter only if his wife dies.) I answer that doing an action to make the divorce and Kidushin take effect at the same time is two Shevusim. We can say that this is forbidden even in the Mikdash. We can say even simpler, that it is better to minimize Shevus. Through Kidushin before Yom Kipur and divorce on Yom Kipur, he causes only one Shevus.

i. Igros Moshe (OC 3 44): R. Akiva Eiger learned from the Bartenura, who says that two Shevusim are more stringent, and are forbidden Bein ha'Shemashos. Tosfos (35a DH Bo'i) does not distinguish. He must have another answer to explain Yoma 13b! Tosfos (13b DH ul'Chada) says that the Yerushalmi says that R. Yehudah holds that he was not Mekadesh a second wife, just they prepared a girl. If his wife would die, he would be Mekadesh her on Yom Kipur. Even though this is Shevus, it is permitted in the Mikdash. If one may make a Kinyan to take effect on Shabbos, why wasn't he Mekadesh her from before Yom Kipur, to take effect after his wife will die?

i. Igros Moshe (ibid.): R. Akiva Eiger says that the Gemara requires that the Kohen Gadol's wife be Nesu'ah. They could do also Chupah on Erev Yom Kipur to take effect when his wife dies, if not that taking effect on Yom Kipur is Shevus. I say that we cannot make Chupah to take effect later, and until then she is Arusah, because Kidushin and Nisu'in are not separate Kinyanim. Rather, Kidushin is the Kinyan, and Nisu'in is a Metzi'us (situation). The Torah obligates laws of marriage only after he brought her to his house. Bitul, Tanai and taking effect later do not apply to Nisu'in. It cannot take effect before Kidushin did. We can ask that the Kidushin should be on Erev Yom Kipur, and the Chupah on Yom Kipur, to transgress only one Shevus, and not two. (The Yerushalmi holds that Chupah is valid even if Bi'ah is forbidden at the time.) Rather, we must say that when he is Mekadesh her in the Chupah on Yom Kipur, this is considered only one Isur. Therefore, there is no proof from the Yerushalmi. I assumed that just like an Arusah is not called "Beiso" to be Machshir a Kohen Gadol for Avodah, she is not called "Beiso" to disqualify a Kohen Gadol with one other wife (a Nesu'ah). This requires investigation. Amora'im, and also Rashi and Tosfos, argue about whether Nisu'in is a Kinyan or a Metzi'us. R. Akiva Eiger holds that it is a Kinyan.

i. B'Tzel ha'Chachmah (3:31:9): One should be more stringent about two Isurim mid'Rabanan than one, even where Chachamim did not say so. Rashi must hold that since another Isur mid'Rabanan was added (when Rav Chisda's daughter became Mekudeshes), one must distance more from her. Why does the Tosfos Rid disagree? In particular, ha'Makneh (81b Rashi DH v'Dar) says that we discuss Kiruv Ervah that the Torah forbids. It seems that Tosfos Rid holds that the Isur to put her in his lap is to distance from Ervah, so it is only one Isur, even if it pertains to several Arayos. This is unlike Temurah 27a. Even though Temurah is one Aveirah, each animal is forbidden by itself, even though it is all from one speech. It is also unlike the Bartenura's case of two Shevusim Bein ha'Shemashos.

i. Minchas Yitzchak (3:24): Yoma 34a discussed putting hot metal in the Mikveh for the Kohen Gadol. Perhaps it is forbidden due to Tziruf (solidifying the metal). Why didn't it mention extinguishing a metal coal? The Riva (in Tosfos Yeshanim 36a Sof DH Hani) asked that one may extinguish a metal coal to avoid damage to the Rabim, but not for an individual. He answered that Ein Shevus b'Mikdash. Tosfos Yeshanim disagrees. Rather, the metal was not so hot. Hagahos Mordechai did not want to say so, since it is hot enough for Tziruf. R. Akiva Eiger says that Chachamim decreed about two Shevusim in the Mikdash. If so, likewise, two Shevusim are not permitted for sickness or pain. We must say that we permit two Shevusim (Tziruf and extinguishing) because there are two reasons to permit (Ein Shevus b'Mikdash, and weakness of the Kohen Gadol). The Gemara asked only from Tziruf, for it thought that it is mid'Oraisa.

i. Minchas Yitzchak (7:42): If it is forbidden because both Shevusim come at the same time, the Kohen Gadol could enter the Beis ha'Keneses once to cause divorce to take effect, and another time to make the Kidushin take effect. Rather, it is best to minimize Shevusim. There was a Hava Amina that transgressing two Shevusim at once is no worse than one Shevus. Even ha'Ozer answered that this is not so. Sha'ar Efrayim (26) forbids two Shevusim that precede the Mitzvah. It does not depend on coming together. Teshuvas R. Akiva Eiger cites Even ha'Ozer, and R. Akiva Eiger (on Eruvin Mishnah 3:3) cites Sha'ar Efrayim, and he did not mention that they disagree. Also, it is not so clear that moving the knife comes together with breaking the cabinet.

i. Minchas Yitzchak (ibid.): The Sha'ar ha'Melech (Eruvin 1:22, b'Sof) asked that according to the Bartenura, why forced the Gemara to say that Sumchus holds like Rabanan? To permit an Eruv of Terumah, one must retract the designation, and then tithe it, i.e. two Shevusim! We can answer like Even ha'Ozer, that two Shevusim at different times are permitted. It seems that Tosfos and other Meforshim disagree with the Bartenura, for they sought other answers.