Yevamot 29 - Statement of intent
If there are two brothers who are married to two sisters, and a third brother, a bachelor, and one of the married brothers dies, the bachelor now has to do a mitzvah of yibum or chalitzah with the widow.
Although the mitzvah of yibum simply means that the brother lives with the widow, the Sages established an additional "statement of intent to marry," which looks like a betrothal. The bachelor acts as proper and makes this statement. However, then the second brother dies. What is the situation of yibum now?
Beit Shammai see no problem: he can keep his wife, to which he made a statement, and the other one - she is his wife's sister - does not need either a yibum or a chalitzah. That is because Beit Shammai regard a statement as a valid betrothal, which makes them husband and wife. Normally, before they can live together, there must be a marriage ceremony, but here, because yibum already allows them that, it is not required.
However, Beit Hillel say that the statement only looks as betrothal, but being that it is not a real one, but only an action instituted by the Sages for the sake of propriety, she his not his legal wife. Therefore, he cannot keep her - because there is another sister, with whom he is connected with the bond of yibum , nor can he marry that sister, because of the same bond, plus his additional statement; in both cases he is as if marrying his wife's sister, which is forbidden. Therefore, he must do a chalitzah with the first sister but also give her a divorce document (Get), because of his prior statement. He then needs to do chalitzah with the other sister. He is thus left without any wife through no fault of his own.
Art: The Betrothal by Jose Juarez