Biconditional elimination allows one to infer a conditional

Material conditional

The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...

 from a biconditional: if ( A ↔ B ) is true, then one may infer either direction of the biconditional, ( A → B ) and ( B → A ).

For example, if it's true that I'm breathing if and only if

If and only if

In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....

I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing.

Formally:
also