Theorem anbi1cd

Description: Introduce a proposition as left conjunct on the left-hand side and right conjunct on the right-hand side of an equivalence. Deduction form. (Contributed by Peter Mazsa, 22-May-2021)

	Ref	Expression
Hypothesis	anbi1cd.1	|- ( ph -> ( ps <-> ch ) )
Assertion	anbi1cd	|- ( ph -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		anbi1cd.1	|- ( ph -> ( ps <-> ch ) )
2	1	anbi2d	|- ( ph -> ( ( th /\ ps ) <-> ( th /\ ch ) ) )
3	2	biancomd	|- ( ph -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )