Theorem pm5.32dar

Description: Reverse distribution of implication over biconditional (deduction form). (Contributed by Zhi Wang, 6-Sep-2024)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.32dar.1	|- ( ph -> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )
2		pm5.32	|- ( ( ps -> ( ch <-> th ) ) <-> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )
3	1 2	sylibr	|- ( ph -> ( ps -> ( ch <-> th ) ) )
4	3	imp	|- ( ( ph /\ ps ) -> ( ch <-> th ) )