Theorem mpbiran4d

Description: Equivalence with a conjunction one of whose conjuncts is a consequence of the other. Deduction form. (Contributed by Zhi Wang, 27-Sep-2024)

	Ref	Expression
Hypotheses	mpbiran3d.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
	mpbiran4d.2	|- ( ( ph /\ th ) -> ch )
Assertion	mpbiran4d	|- ( ph -> ( ps <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		mpbiran3d.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
2		mpbiran4d.2	|- ( ( ph /\ th ) -> ch )
3	1	biancomd	|- ( ph -> ( ps <-> ( th /\ ch ) ) )
4	3 2	mpbiran3d	|- ( ph -> ( ps <-> th ) )