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

Metamath Proof Explorer

Theorem imp

Description: Importation inference. (Contributed by NM, 3-Jan-1993) (Proof shortened by Eric Schmidt, 22-Dec-2006)

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

Step	Hyp	Ref	Expression
1		imp.1	$⊢ φ \to (ψ \to χ)$
2		df-an	$⊢ (φ \land ψ) \leftrightarrow \neg (φ \to \neg ψ)$
3	1	impi	$⊢ \neg (φ \to \neg ψ) \to χ$
4	2 3	sylbi	$⊢ (φ \land ψ) \to χ$