- Biconditional elimination
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 ifI'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.
( A ↔ B ) ∴ ( A → B )
( A ↔ B ) ∴ ( B → A )
If and only if
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