Theorem imdi 378

Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem imdi

Step	Hyp	Ref	Expression
1		ax-2 7	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2		pm2.86 108	. 2 |- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
3	1, 2	impbii 199	1 |- ( ( ph -> ( ps -> ch ) ) <-> ( ( ph -> ps ) -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196

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 197

This theorem is referenced by:  pm5.41  379  orimdi  892  bnj1174  31071  ifpim23g  37840