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We begin Perek III with another new Mishna. It teaches about the case of four brothers, two of whom married two sisters and then died, leaving them childless. The levirate bond that exists between each brother and sister precludes them from marrying, due to the forbidden sexual relationships between brothers and their wives' sisters (the levirate bond serves as a reminder of the sexual bond between the brothers and both women). Thus the women must perform chalitza; if they married before consulting the court, they must divorce.
Rav rules that when three sisters fall to Yibum to two brothers, one brother does Chalitzah with one sister, the other brother does Chalitzah with the second sister, and then both brothers must do Chalitzah with the third sister.
Our Daf infers from this ruling that Chalitzah with one's "Achos Chalutzaso" (the sister of a woman with whom he did Chalitzah) is considered a "Chalitzah Pesulah," and whenever a Chalitzah Pesulah is performed it must be done by all of the brothers in order to take effect and release the woman from the requirement of Yibum (because the bond of Zikah is too strong to be broken by a Chalitzah Pesulah).
A "Chalitzah Pesulah" is defined as a Chalitzah done by a brother who was not permitted to do Yibum.
The Rambam (Yibum 7:10) describes another case of chalitza pesulah. A man dies and leaves two wives, and one is forbidden to his brother with the strength of a lav. If he does chalitza to that wife, it is not good enough to work for the wife who was permitted to him, and he has to do chalitza to her as well.
We explore Karate traditions and levirate marriage and the remarkable fact that marriages between Karaites and Rabbinates continued as late as the RAMBAM who paskened their marriages were kosher but their gitten were not.
How does their exegesis regarding yibum differ from the rabbinic tradition and how much closer were they to the pshat?