Logical Biconditional - Rules of Inference - 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, ( 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 )

Read more about this topic:  Logical Biconditional, Rules of Inference

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