Theorem pm5.32d

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 29-Oct-1996)

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

Proof

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