Theorem pm5.32ri

Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 12-Mar-1995)

	Ref	Expression
Hypothesis	pm5.32i.1	|- ( ph -> ( ps <-> ch ) )
Assertion	pm5.32ri	|- ( ( ps /\ ph ) <-> ( ch /\ ph ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.32i.1	|- ( ph -> ( ps <-> ch ) )
2	1	pm5.32i	|- ( ( ph /\ ps ) <-> ( ph /\ ch ) )
3		ancom	|- ( ( ps /\ ph ) <-> ( ph /\ ps ) )
4		ancom	|- ( ( ch /\ ph ) <-> ( ph /\ ch ) )
5	2 3 4	3bitr4i	|- ( ( ps /\ ph ) <-> ( ch /\ ph ) )