Theorem 3anbi1i

Description: Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006)

	Ref	Expression
Hypothesis	3anbi1i.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	3anbi1i	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		3anbi1i.1	$$⊢\phi \leftrightarrow \psi$$
2		biid	$$⊢\chi \leftrightarrow \chi$$
3		biid	$$⊢\theta \leftrightarrow \theta$$
4	1 2 3	3anbi123i	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$