Theorem anbi1i

Description: Introduce a right conjunct to both sides of a logical equivalence. (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)

	Ref	Expression
Hypothesis	anbi.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	anbi1i	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢\chi \to \left(\phi \leftrightarrow \psi \right)$$
3	2	pm5.32ri	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$