Theorem anbi12i

Description: Conjoin both sides of two equivalences. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	anbi12.1	|- ( ph <-> ps )
	anbi12.2	|- ( ch <-> th )
Assertion	anbi12i	|- ( ( ph /\ ch ) <-> ( ps /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		anbi12.1	|- ( ph <-> ps )
2		anbi12.2	|- ( ch <-> th )
3	1	anbi1i	|- ( ( ph /\ ch ) <-> ( ps /\ ch ) )
4	2	anbi2i	|- ( ( ps /\ ch ) <-> ( ps /\ th ) )
5	3 4	bitri	|- ( ( ph /\ ch ) <-> ( ps /\ th ) )