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Theorem bi3 179
Description: Property of the biconditional connective. (Contributed by NM, 11-May-1999.)
Assertion
Ref Expression
bi3 ((φψ) → ((ψφ) → (φψ)))

Proof of Theorem bi3
StepHypRef Expression
1 df-bi 177 . . 3 ¬ (((φψ) → ¬ ((φψ) → ¬ (ψφ))) → ¬ (¬ ((φψ) → ¬ (ψφ)) → (φψ)))
2 simprim 142 . . 3 (¬ (((φψ) → ¬ ((φψ) → ¬ (ψφ))) → ¬ (¬ ((φψ) → ¬ (ψφ)) → (φψ))) → (¬ ((φψ) → ¬ (ψφ)) → (φψ)))
31, 2ax-mp 5 . 2 (¬ ((φψ) → ¬ (ψφ)) → (φψ))
43expi 141 1 ((φψ) → ((ψφ) → (φψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  impbii  180  impbidd  181  dfbi1  184  bisym  281
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