Midrash for Bekhorot 91:5

כי ההוא דמקרי דרדקי אדריה רב אחא דקא פשע בינוקי ואהדריה רבינא דלא אשכח דהוה דייק כוותיה:

AND ONE WHO MAKES HIMSELF UNCLEAN THROUGH THE DEAD etc. What is the difference between the case here, where merely an undertaking suffices and there [where a priest contracts an illegal marriage] that we impose a votary prohibition on him? - There [in the latter case] his passion overpowers him.<span class="x" onmousemove="('comment',' Therefore we do not merely rely on an undertaking that he will divorce her but there must be a votary prohibition forbidding any benefit to be derived from her. But where this consideration is absent, we rely on an undertaking given by him.');">³</span>

Sifrei Devarim