Theorem biadaniALT

Description: Alternate proof of biadani not using biadan . (Contributed by BJ, 4-Mar-2023) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		biadani.1	|- ( ph -> ps )
2		pm5.32	|- ( ( ps -> ( ph <-> ch ) ) <-> ( ( ps /\ ph ) <-> ( ps /\ ch ) ) )
3	1	pm4.71ri	|- ( ph <-> ( ps /\ ph ) )
4	3	bibi1i	|- ( ( ph <-> ( ps /\ ch ) ) <-> ( ( ps /\ ph ) <-> ( ps /\ ch ) ) )
5	2 4	bitr4i	|- ( ( ps -> ( ph <-> ch ) ) <-> ( ph <-> ( ps /\ ch ) ) )