Theorem imimorb 921

Description: Simplify an implication between implications. (Contributed by Paul Chapman, 17-Nov-2012.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Assertion

Ref	Expression
imimorb	|- ( ( ( ps -> ch ) -> ( ph -> ch ) ) <-> ( ph -> ( ps \/ ch ) ) )

Proof of Theorem imimorb

Step	Hyp	Ref	Expression
1		bi2.04 376	. 2 |- ( ( ( ps -> ch ) -> ( ph -> ch ) ) <-> ( ph -> ( ( ps -> ch ) -> ch ) ) )
2		dfor2 427	. . 3 |- ( ( ps \/ ch ) <-> ( ( ps -> ch ) -> ch ) )
3	2	imbi2i 326	. 2 |- ( ( ph -> ( ps \/ ch ) ) <-> ( ph -> ( ( ps -> ch ) -> ch ) ) )
4	1, 3	bitr4i 267	1 |- ( ( ( ps -> ch ) -> ( ph -> ch ) ) <-> ( ph -> ( ps \/ ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196   \/ wo 383

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  df-or 385

This theorem is referenced by: (None)