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	$$⊢\phi \leftrightarrow \psi$$
Assertion	anbi2ci	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\chi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi.1	$$⊢\phi \leftrightarrow \psi$$
2	1	anbi1i	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$
3	2	biancomi	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\chi \wedge \psi \right)$$