Before us is the first Mishnah in the third chapter of Maseches Yevamos, which opens with a case of four brothers and discusses when a yevamah performs chalitzah rather than entering into yibum, and what her status is after the fact if yibum has already taken place.
The words of the Mishnah:
"Arba'ah achim" - the case involves a family with four brothers.
"Shenayim nesu'im shtei achayos" - two of the brothers are married to two sisters.
"U'meisu ha'nesu'im es ha'achayos" - the two brothers who were married to the sisters died, and their two wives fall to yibum before the two remaining brothers.
"Harei eilu cholotzos v'lo misyabmos" - they have only chalitzah, and they cannot enter into yibum.
The reason for this:
Each of the two yevamos is the sister of a woman to whom the brother has a zikah. The yavam is bound to one of them, but he also has a zikah to her sister, and since she is the sister of the woman bound to him, she is treated like his wife's sister, and by rabbinic law he cannot marry her through yibum. Nevertheless, the Torah obligation of yibum still exists, and therefore chalitzah must be performed.
"V'im kadmu v'chansu - yotzi'u":
If they transgressed and acted improperly, going ahead and taking them in marriage when they were not permitted to do so, they must divorce them with a get, and they cannot remain married to them.
The difference from the cases in the previous chapter:
In the previous chapter we learned about a man who married one of two sisters but it is unknown which one, and he died leaving two brothers: one of them performs chalitzah and the other performs yibum, since the chalitzah removes the zikah. And if they went ahead and married both of them, we do not require them to divorce, and they may remain married. The same is true in the similar but more complicated case that follows it, where too they were permitted to remain married, even though there as well the issue is the sister of the woman bound to him.
The difference is clear: the cases in the previous chapter were cases of doubt regarding the sister of the woman bound to him. We do not know, and it is possible that he in fact married the one who was permitted to him, since only one of them is bound to him, and it may well be that he performed yibum with her properly. Because of that doubt, if they transgressed and married the one they should not have married, we permit them to remain married. But here, where it is certain that she is the sister of the woman bound to him, we say that even after the fact, once the act is done, they must divorce.
The opinion of Rabbi Eliezer:
Rabbi Eliezer disagrees with the first Tanna and holds that the matter is not clear-cut, and according to him Beis Shammai and Beis Hillel disagreed about it:
"Beis Shammai omrim yekayemu" - if after the fact they married them, they may remain married and need not divorce.
"U'Beis Hillel omrim yotzi'u" - since the yibum was performed in a forbidden manner, they must divorce.
The Beraisa in the Gemara:
It is interesting to note that the Gemara brings a Beraisa that disagrees with Rabbi Eliezer's version. There Abba Shaul says the opposite: Beis Shammai are the stringent ones, as they usually are, and they are the ones who say that they must divorce; while Beis Hillel are the lenient ones, and they are the ones who say "yekayemu" - that they may remain married to one another.
In summary: when four brothers include two who were married to two sisters and those two died, their wives perform chalitzah and do not enter into yibum, because each of them is the sister of the woman bound to the yavam; the chalitzah is performed because of the Torah obligation of yibum, while yibum itself was forbidden by rabbinic law. And if they went ahead and married them, they must divorce, unlike the cases of doubt in the previous chapter, where the ruling was lenient after the fact. Rabbi Eliezer reports here a dispute between Beis Shammai and Beis Hillel, while Abba Shaul in the Beraisa reverses the positions.