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

Metamath Proof Explorer

Theorem ord

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994)

		Ref	Expression
	Hypothesis	ord.1	$⊢ φ \to (ψ \lor χ)$
	Assertion	ord	$⊢ φ \to (\neg ψ \to χ)$

Step	Hyp	Ref	Expression
1		ord.1	$⊢ φ \to (ψ \lor χ)$
2		df-or	$⊢ (ψ \lor χ) \leftrightarrow (\neg ψ \to χ)$
3	1 2	sylib	$⊢ φ \to (\neg ψ \to χ)$