Hi,
I have some colleagues who are not aware of this "basic" reasoning. But I admit I had to make a search to find the formal demonstration.
Having an original proposition, P0:
A⇒B.
It is defined as: ¬A∨B, where "¬" means "Not-", and "∨" means "Or"; but I don't either have this demonstration or really understand this (your help would be appreciated).
Then:
⟺ ¬A∨¬(¬B), (only a double negation on B - what remain the same)
⟺ ¬(¬B)∨¬A, (the or is commutative)
⟺ ¬B⇒¬A, (following the above definition).
I think the definition follows a sets-logic, but if you can help me in helping my "atheist brother", I'll thank you.