Theorem imimorb 847

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		bi2.04 350	. 2 |- (((ps -> ch) -> (ph -> ch)) <-> (ph -> ((ps -> ch) -> ch)))
2		dfor2 400	. . 3 |- ((ps \/ ch) <-> ((ps -> ch) -> ch))
3	2	imbi2i 303	. 2 |- ((ph -> (ps \/ ch)) <-> (ph -> ((ps -> ch) -> ch)))
4	1, 3	bitr4i 243	1 |- (((ps -> ch) -> (ph -> ch)) <-> (ph -> (ps \/ ch)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   \/ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by: (None)