Theorem bianim

Description: Exchanging conjunction in a biconditional. (Contributed by Peter Mazsa, 31-Jul-2023)

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

Proof

Step	Hyp	Ref	Expression
1		bianim.1	|- ( ph <-> ( ps /\ ch ) )
2		bianim.2	|- ( ch -> ( ps <-> th ) )
3	2	pm5.32ri	|- ( ( ps /\ ch ) <-> ( th /\ ch ) )
4	1 3	bitri	|- ( ph <-> ( th /\ ch ) )