Theorem anbi12ci

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

	Ref	Expression
Hypotheses	anbi12.1	$$⊢\phi \leftrightarrow \psi$$
	anbi12.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	anbi12ci	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\theta \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi12.1	$$⊢\phi \leftrightarrow \psi$$
2		anbi12.2	$$⊢\chi \leftrightarrow \theta$$
3	1 2	anbi12i	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \theta \right)$$
4	3	biancomi	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\theta \wedge \psi \right)$$