Theorem biadanii

Description: Inference associated with biadani . Add a conjunction to an equivalence. (Contributed by Jeff Madsen, 20-Jun-2011) (Proof shortened by BJ, 4-Mar-2023)

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

Proof

Step	Hyp	Ref	Expression
1		biadani.1	|- ( ph -> ps )
2		biadanii.2	|- ( ps -> ( ph <-> ch ) )
3	1	biadani	|- ( ( ps -> ( ph <-> ch ) ) <-> ( ph <-> ( ps /\ ch ) ) )
4	2 3	mpbi	|- ( ph <-> ( ps /\ ch ) )