Theorem pm5.32da

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 9-Dec-2006)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.32da.1	|- ( ( ph /\ ps ) -> ( ch <-> th ) )
2	1	ex	|- ( ph -> ( ps -> ( ch <-> th ) ) )
3	2	pm5.32d	|- ( ph -> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )