He will marry his daughter off to his brother (the Torah law allows marriage with the niece.) Then, when his brother dies, he gets to marry his daughter as his brother's wife or a "yevamah." True, there is a prohibition against marrying one's daughter, but it is overwritten by a positive commandment to marry a yevamah.
His source? Two verses: "You should not wear wool and linen together" and next to it, "You shall fringes on your garment." For your fringes (tzitzit), you can use wool and linen together. In fact, that is what they did in the Temple, making the priests' belts. This teaches us that "do" overwrites "don't do."
He seems to have built his case? We answer that "do" overwrite "don't do" only for relatively light prohibitions, such as wearing wool and linen together. Marrying one's daughter - or any other similar ban - is more strict. So even the mitzvah of yibum does not help him turn the forbidden into permitted.
Art: Henri Rouart and his Daughter Helene by Edgar Degas