This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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) (Proof shortened by Peter Mazsa, 24-Feb-2026)

		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	1	baibd	\|- ( ( ph /\ ch ) -> ( ps <-> th ) )
3	2	pm5.32da	\|- ( ph -> ( ( ch /\ ps ) <-> ( ch /\ th ) ) )