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Metamath Proof Explorer

Theorem imdistani

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994)

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

Step	Hyp	Ref	Expression
1		imdistani.1	$⊢ φ \to (ψ \to χ)$
2	1	anc2li	$⊢ φ \to (ψ \to (φ \land χ))$
3	2	imp	$⊢ (φ \land ψ) \to (φ \land χ)$