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Metamath Proof Explorer

Theorem anbi12i

Description: Conjoin both sides of two equivalences. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	anbi12.1	$⊢ φ \leftrightarrow ψ$
	anbi12.2	$⊢ χ \leftrightarrow θ$
Assertion	anbi12i	$⊢ (φ \land χ) \leftrightarrow (ψ \land θ)$

Step	Hyp	Ref	Expression
1		anbi12.1	$⊢ φ \leftrightarrow ψ$
2		anbi12.2	$⊢ χ \leftrightarrow θ$
3	2	anbi2i	$⊢ (φ \land χ) \leftrightarrow (φ \land θ)$
4	3 1	bianbi	$⊢ (φ \land χ) \leftrightarrow (ψ \land θ)$