Theorem anbi1

Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	anbi1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
2	1	anbi1d	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)\right)$$