I'm in a debate with my math teacher over this, and she just doesn't understand what I'm asking. It's actually a pretty simple question. Is there a rule, law, or algebraic solution that states:

if then

I was marked incorrectly on an assignment for refusing to make that assumption, and I refused to make that assumption because I was not able to find such a rule anywhere online or in the textbook. I don't mind being wrong if I actually am incorrect, I just want proof. Thanks in advance.