Theorem mpbirand

Description: Detach truth from conjunction in biconditional. (Contributed by Glauco Siliprandi, 3-Mar-2021)

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

Proof

Step	Hyp	Ref	Expression
1		mpbirand.1	|- ( ph -> ch )
2		mpbirand.2	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
3	1	biantrurd	|- ( ph -> ( th <-> ( ch /\ th ) ) )
4	2 3	bitr4d	|- ( ph -> ( ps <-> th ) )