Theorem mpbiran2d

Description: Detach truth from conjunction in biconditional. Deduction form. (Contributed by Peter Mazsa, 24-Sep-2022)

	Ref	Expression
Hypotheses	mpbiran2d.1	|- ( ph -> th )
	mpbiran2d.2	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
Assertion	mpbiran2d	|- ( ph -> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		mpbiran2d.1	|- ( ph -> th )
2		mpbiran2d.2	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
3	2	biancomd	|- ( ph -> ( ps <-> ( th /\ ch ) ) )
4	1 3	mpbirand	|- ( ph -> ( ps <-> ch ) )