TITLE: Proving an if and only if statement
QUESTION [8 upvotes]: Suppose I am trying to prove a statement in the form A if and only if B. I know I need to prove that 

If A, then B
If B, then A

I know that 1 is equivalent to proving "If not B, then not A". 
My question is: When proving A if and only if B, is it permissible to prove "if not B, then not A" and then "if B, then A." 
I have seen many people prove A iff B by showing "If not A, then not B" and then "If not B, then not A," but never the way I described, which is why I am asking if it is okay.

REPLY [6 votes]: Yes that is perfectly fine. A implies B is logically equivalent to "not B, then not A".