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Metamath Proof Explorer

Theorem anbi1cd

Description: Introduce a proposition as left conjunct on the left-hand side and right conjunct on the right-hand side of an equivalence. Deduction form. (Contributed by Peter Mazsa, 22-May-2021)

		Ref	Expression
	Hypothesis	anbi1cd.1	$⊢ φ \to (ψ \leftrightarrow χ)$
	Assertion	anbi1cd	$⊢ φ \to ((θ \land ψ) \leftrightarrow (χ \land θ))$

Proof

Step	Hyp	Ref	Expression
1		anbi1cd.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2	1	anbi2d	$⊢ φ \to ((θ \land ψ) \leftrightarrow (θ \land χ))$
3	2	biancomd	$⊢ φ \to ((θ \land ψ) \leftrightarrow (χ \land θ))$