Theorem anbi2ci

Description: Variant of anbi2i with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011)

	Ref	Expression
Hypothesis	anbi.1	|- ( ph <-> ps )
Assertion	anbi2ci	|- ( ( ph /\ ch ) <-> ( ch /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		anbi.1	|- ( ph <-> ps )
2	1	anbi1i	|- ( ( ph /\ ch ) <-> ( ps /\ ch ) )
3	2	biancomi	|- ( ( ph /\ ch ) <-> ( ch /\ ps ) )