לזכות רבקה אסתר בת אליהו פרץ לברכה והצלחה ושמחה תמיד!
In order to transgress the איסור of not shechting a mother animal and the child on the same day - אותו ואת בנו לא תשחטו ביום אחד, both shchitas must be valid. Now, if one shechts a korban and doesn't sprinkle the blood he invalidates the korban.
What is the din if one shechted a korban shlamim and then shechted the child of the korban. Should he then not sprinkle the blood of the mother in order to save himself from the איסור of אותו ואת בנו. On the other hand he would then be invalidating the mitzva. Do we invalidate a mitzva in order to save ourselves from an aveirah?
[What do you call it when a girl tells a boy (or vice versa) that she doesn't want to see him anymore? InvaliDATEd.]
R' Akiva Eiger [Chullin 81a] says that on one hand one shouldn't sprinkle the blood in order to save himself from an aveirah. On the other hand he says that when you have a mitzva to do - you do it without taking the consequences of the resulting aveirah into account.
The Rashba [Gittin 83a] says that if one divorces a woman on condition that he doesn't eat matza and then she marries someone else - she may NOT fulfill the mitzva of eating matza because that would result in her being married to the first man retroactively and having lived in sin with man number two.
That doesn't seem consistent with side two of R' A.E. [that we do mitzvos without taking the consequences into account]. Or maybe there is a חילוק?
Think about it.
[Or listen to a recent shiur on the topic. Or both:-)].