Theorem pm5.32rd

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 25-Dec-2004)

	Ref	Expression
Hypothesis	pm5.32d.1	|- ( ph -> ( ps -> ( ch <-> th ) ) )
Assertion	pm5.32rd	|- ( ph -> ( ( ch /\ ps ) <-> ( th /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.32d.1	|- ( ph -> ( ps -> ( ch <-> th ) ) )
2	1	pm5.32d	|- ( ph -> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )
3		ancom	|- ( ( ch /\ ps ) <-> ( ps /\ ch ) )
4		ancom	|- ( ( th /\ ps ) <-> ( ps /\ th ) )
5	2 3 4	3bitr4g	|- ( ph -> ( ( ch /\ ps ) <-> ( th /\ ps ) ) )