Yevamot, Chapter Fourteen, Mishnah Five
1) If two brothers of sound senses were married to two sisters one of whom was deaf and the other of sound senses, and the brother of sound senses, the husband of the deaf sister, died, what should the brother of sound senses, the husband of the sister who was of sound senses, do?
a) [Nothing, since she is] exempt because she is his wifes sister.
2) If the brother of sound senses, the husband of the sister who was of sound senses, died, what should the brother of sound senses, the husband of the deaf sister, do?
a) He must release his wife with a get and his brothers wife by halitzah.
Section one: In this scenario two brothers of sound senses are married to two sisters, one of whom is deaf. This means that one of the marriages is deoraita and the other derabbanan. If the brother married to the deaf sister dies, the deaf sister becomes liable for yibbum or halitzah with the other brother. Since this is forbidden because he is deoraita married to her sister, she is totally exempt.
Section two: In this case, the brother married to the sister of sound senses dies. This marriage was deoraita and therefore her ties to the yavam are of a deoraita status. The yavam is only derabbanan married to her sister, since she is deaf. Therefore, the yevamah is not exempt from yibbum or halitzah. Nevertheless the yavam cannot have yibbum with her because he is married to her sister. The only solution is for him to divorce his wife, who is forbidden to him as the sister of a woman tied to him through yibbum. Then he must have halitzah with the other sister. He cannot have yibbum because he was married to her sister, even though the marriage was only derabbanan.