Yevamos, Chapter 3, Mishnah 5. We have already examined the concept of ma'amar - the rabbinic betrothal that a yavam performs with his yevamah before actually fulfilling the mitzvah of yibum. Now we turn to the question: what is the status of a yevamah with whom the yavam has performed ma'amar? Do we view them as married, or not? Beis Shammai and Beis Hillel disagree about this in our Mishnah.
The words of the Mishnah:
"Sheloshah achim, shenayim mehem nesu'in lishtei achayos ve'echad mufneh" - two brothers are married to two sisters, and the third brother is unmarried.
"Meis echad miba'alei achayos" - one of the husbands of the sisters dies, and his widow falls to yibum.
"Ve'asah bah mufneh ma'amar" - the third brother does not perform yibum with her, but rather performs ma'amar with her, a rabbinic betrothal, with the expectation of fulfilling yibum, but in the end he does not carry out the yibum.
"Ve'achar kach meis achiv hasheini" - afterwards the second brother, who is married to the other sister, also dies, and his wife falls before him for yibum.
To picture the case: Reuven and Shimon are married to two sisters, and Levi is unmarried. Reuven dies, and Levi performs ma'amar with his widow. Afterwards Shimon dies, and his wife now falls to Levi for yibum - and she is the sister of the woman bound to him. And that is precisely the question: is she indeed considered the sister of the woman bound to him, or not?
The view of Beis Shammai:
"Beis Shammai omrim: ishto imo, vehalah teitzei mishum achos ishah" - from the moment Levi performed ma'amar with Reuven's widow, she is his wife. Therefore Shimon's widow, who is the sister of the woman with whom he performed ma'amar, goes free without any obligation of yibum or chalitzah, because she is his wife's sister and thus forbidden to him as an ervah. Beis Shammai view the ma'amar as though he had married her completely, and for that reason the second widow, her sister, is an ervah when she falls before him and is exempt from yibum.
The view of Beis Hillel:
Beis Hillel hold that the ma'amar creates only a rabbinic bond. On the one hand, the second co-wife may not be taken in yibum, since she is his wife's sister - or at the very least appears to be his wife's sister; and on the other hand, the bond of the ma'amar has already been created with the first widow, Reuven's widow.
"Beis Hillel omrim: motzi ishto b'get uv'chalitzah" - and from here two practical rulings follow:
His wife, the one with whom he performed ma'amar: a get - because the ma'amar is a rabbinic betrothal, and removing it requires a get; and also chalitzah - since Beis Hillel do not view the ma'amar as a complete marriage, and therefore there still remains here a bond of yibum that was never fulfilled, and that bond requires chalitzah.
His brother's wife, Shimon's widow, the sister of the woman with whom he performed ma'amar: chalitzah alone. She cannot be released entirely as Beis Shammai held, who said that he is already married to one sister and the other is an ervah to him with no obligation of yibum at all; for on a Torah level the obligation of yibum still exists, and therefore chalitzah is required. And he cannot perform yibum with her, because of the matter of his wife's sister.
About this situation Chazal said: "Oy lo al ishto ve'oy lo al eishes achiv" - woe to him regarding his wife, the one with whom he performed ma'amar, whom he is required to send away; and woe to him regarding his brother's wife, for her too he cannot take in yibum because of the problem of his wife's sister, and all he can do is perform chalitzah with her.
In summary: in this Mishnah Beis Shammai and Beis Hillel disagree about the status of a yevamah with whom ma'amar was performed. According to Beis Shammai, ma'amar is like a complete marriage, and therefore her sister, who falls afterwards, is an ervah and goes free without yibum and without chalitzah. According to Beis Hillel, ma'amar is only a rabbinic bond: the woman with whom he performed ma'amar he sends away with a get and with chalitzah - a get because of the ma'amar, and chalitzah because of the bond that was never fulfilled; and his brother's wife he releases with chalitzah alone. And about this they said: "Oy lo al ishto ve'oy lo al eishes achiv".