Theorem anbi1ci

Description: Variant of anbi1i with commutation. (Contributed by Peter Mazsa, 7-Mar-2020)

	Ref	Expression
Hypothesis	anbi.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	anbi1ci	$$⊢\left(\chi \wedge \phi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi.1	$$⊢\phi \leftrightarrow \psi$$
2	1	anbi2i	$$⊢\left(\chi \wedge \phi \right)\leftrightarrow \left(\chi \wedge \psi \right)$$
3	2	biancomi	$$⊢\left(\chi \wedge \phi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$