Theorem biadani

Description: Inference associated with biadan . (Contributed by BJ, 4-Mar-2023)

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

Proof

Step	Hyp	Ref	Expression
1		biadani.1	|- ( ph -> ps )
2		biadan	|- ( ( ph -> ps ) <-> ( ( ps -> ( ph <-> ch ) ) <-> ( ph <-> ( ps /\ ch ) ) ) )
3	1 2	mpbi	|- ( ( ps -> ( ph <-> ch ) ) <-> ( ph <-> ( ps /\ ch ) ) )