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Metamath Proof Explorer

Theorem imdistanri

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002)

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

Step	Hyp	Ref	Expression
1		imdistanri.1	$⊢ φ \to (ψ \to χ)$
2	1	com12	$⊢ ψ \to (φ \to χ)$
3	2	impac	$⊢ (ψ \land φ) \to (χ \land φ)$