Theorem bian1d

Description: Adding a superfluous conjunct in a biconditional. (Contributed by Thierry Arnoux, 26-Feb-2017) (Proof shortened by Hongxiu Chen, 29-Jun-2025)

	Ref	Expression
Hypothesis	bian1d.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
Assertion	bian1d	|- ( ph -> ( ( ch /\ ps ) <-> ( ch /\ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		bian1d.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )
2		ibar	|- ( ch -> ( th <-> ( ch /\ th ) ) )
3	2	bicomd	|- ( ch -> ( ( ch /\ th ) <-> th ) )
4	1 3	sylan9bb	|- ( ( ph /\ ch ) -> ( ps <-> th ) )
5	4	ex	|- ( ph -> ( ch -> ( ps <-> th ) ) )
6	5	pm5.32d	|- ( ph -> ( ( ch /\ ps ) <-> ( ch /\ th ) ) )