This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3anbi1i

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

		Ref	Expression
	Hypothesis	3anbi1i.1	$⊢ φ \leftrightarrow ψ$
	Assertion	3anbi1i	$⊢ (φ \land χ \land θ) \leftrightarrow (ψ \land χ \land θ)$

Step	Hyp	Ref	Expression
1		3anbi1i.1	$⊢ φ \leftrightarrow ψ$
2		biid	$⊢ χ \leftrightarrow χ$
3		biid	$⊢ θ \leftrightarrow θ$
4	1 2 3	3anbi123i	$⊢ (φ \land χ \land θ) \leftrightarrow (ψ \land χ \land θ)$