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Theorem imdi 237
Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
imdi ((φ → (ψχ)) ↔ ((φψ) → (φχ)))

Proof of Theorem imdi
StepHypRef Expression
1 ax-2 6 . 2 ((φ → (ψχ)) → ((φψ) → (φχ)))
2 pm2.86 92 . 2 (((φψ) → (φχ)) → (φ → (ψχ)))
31, 2impbii 115 1 ((φ → (ψχ)) ↔ ((φψ) → (φχ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 96
This theorem is referenced by:  pm5.41  238
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 98  ax-ia3 99
This theorem depends on definitions:  df-bi 108
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