Theorem imimorb

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

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

Proof

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