Biconditional elimination

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Biconditional elimination allows one to infer 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 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 )

[edit] See also

• Logical biconditional
• If and only if