**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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### Famous quotes containing the word elimination:

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