Biconditional elimination

Biconditional elimination allows one to infer a conditional from a biconditional: if ( A ↔ B ) is true, then one may infer one direction of the biconditional, either ( A → B ) or ( B → A ).

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

  ( A ↔ B )  
  ∴ ( A → B )

also

  ( A ↔ B )  
  ∴ ( B → A )