Theorem anbi12ci

Description: Variant of anbi12i with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	anbi12.1	|- ( ph <-> ps )
	anbi12.2	|- ( ch <-> th )
Assertion	anbi12ci	|- ( ( ph /\ ch ) <-> ( th /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		anbi12.1	|- ( ph <-> ps )
2		anbi12.2	|- ( ch <-> th )
3	1 2	anbi12i	|- ( ( ph /\ ch ) <-> ( ps /\ th ) )
4	3	biancomi	|- ( ( ph /\ ch ) <-> ( th /\ ps ) )