Before us is Mishnah 7 of the thirteenth chapter of Yevamos, which deals with two brothers married to two sisters, and with situations in which the validity of the marriage of one of them, or of both, is only rabbinic.
The First Case - Two Orphaned Minor Sisters:
The Mishnah opens: "Shnei achim nesu'im lishtei achayos yesomos ketanos, u'meis ba'alah shel achas mehen - teitzei mishum achos ishah" - two adult brothers are married to two orphaned sisters who have no father, and who are minors, so that their marriage rests only on rabbinic kiddushin. The husband of one of them died, and the second brother cannot perform yibum with her, since she is his wife's sister - a forbidden relative with whom yibum does not take effect.
It is worth noting precisely: every component of this case is rabbinic only. His own marriage is rabbinic, the prohibition of a wife's sister that stands against him is rabbinic, and even the potential obligation of yibum is nothing more than rabbinic.
"Vehen shtei chershos":
The law remains the same even when we are not dealing with orphaned minors, but with two adult sisters who are deaf-mutes, whose kiddushin too is only rabbinic.
The Complex Case - "Gedolah U'ketanah":
When the two levels are combined, a more complicated case arises: two brothers are married to two sisters, one an adult whose marriage is biblical, and the other a minor whose kiddushin is rabbinic. Two situations present themselves:
"Meis ba'alah shel ketanah": The minor, whose kiddushin is rabbinic, falls to yibum before the brother who is married to the adult sister with a biblical marriage. She is his wife's sister on the full biblical level - for his wife is married to him biblically, and he is the husband of her sister - and therefore "teitzei haketanah mishum achos ishah", and there is no obligation of yibum with her.
"Meis ba'alah shel gedolah": The adult sister falls to yibum, and her obligation of yibum is biblical. The brother, however, is married to the minor with rabbinic kiddushin only, and therefore the yevamah is forbidden to him as his wife's sister - but on the rabbinic level alone. Here a biblical obligation of yibum and a rabbinic prohibition of a wife's sister stand facing one another, and the question is which prevails.
The Dispute of the Tannaim in This Case:
Rabbi Eliezer: "Melamdin es haketanah shetema'ein bo" - we instruct the minor who is married to the yavam to refuse the marriage, and by doing so the bond of her marriage dissolves. And since with a minor who refused the marriage a man is permitted to her relatives, the yevamah is no longer in the category of his wife's sister, and she is permitted for yibum.
Rabban Gamliel: "Im mi'anah, mi'anah" - we do not instruct her at the outset to refuse, for this is not a desirable path; but if she refused on her own, he may perform yibum with the adult sister. "Ve'im lo - tamtin ad shetagdil": if she does not wish to refuse, she remains in her rabbinic marriage until she matures and reaches the age of mitzvos, and then her marriage becomes a biblical marriage, "veteitzei halazu mishum achos ishah" - the yevamah goes free, for now she has become his wife's sister in the fullest sense, on the biblical level, a forbidden relative with whom there is no yibum.
Rabbi Yehoshua: He accepts neither of the two solutions, and says: "Oy lo al ishto ve'oy lo al eishes achiv" - woe to him regarding his wife, whom he is forced to part from, and woe to him regarding his brother's wife, with whom he cannot perform yibum. Rather, "motzi es ishto b'get ve'es eishes achiv bachalitzah": his minor wife he must divorce with a get, since he has a biblical bond to her sister, so that his wife is forbidden to him as the sister of the woman bound to him, and he does not hold of the approach of instructing her to refuse; and his brother's wife, the yevamah, he cannot take in yibum, for once he has given a get to his wife, the yevamah is the sister of his divorcee, and therefore he must perform chalitzah with her.
And so, according to Rabbi Yehoshua, this is how the situation is handled: the brother parts from his minor wife with a get, and releases his brother's wife through chalitzah.