Theorem anbi2

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013)

	Ref	Expression
Assertion	anbi2	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\chi \wedge \phi \right)\leftrightarrow \left(\chi \wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
2	1	anbi2d	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\chi \wedge \phi \right)\leftrightarrow \left(\chi \wedge \psi \right)\right)$$