Theorem imdi 168

Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
imdi	|- ((ph -> (ps -> ch)) <-> ((ph -> ps) -> (ph -> ch)))

Proof of Theorem imdi

Step	Hyp	Ref	Expression
1		ax-2 5	. 2 |- ((ph -> (ps -> ch)) -> ((ph -> ps) -> (ph -> ch)))
2		pm2.86 69	. 2 |- (((ph -> ps) -> (ph -> ch)) -> (ph -> (ps -> ch)))
3	1, 2	impbi 157	1 |- ((ph -> (ps -> ch)) <-> ((ph -> ps) -> (ph -> ch)))

Syntax hints:   -> wi 3   <-> wb 146

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147

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