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Metamath Proof Explorer

Theorem 3ori

Description: Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006)

		Ref	Expression
	Hypothesis	3ori.1	$⊢ (φ \lor ψ \lor χ)$
	Assertion	3ori	$⊢ (\neg φ \land \neg ψ) \to χ$

Step	Hyp	Ref	Expression
1		3ori.1	$⊢ (φ \lor ψ \lor χ)$
2		ioran	$⊢ \neg (φ \lor ψ) \leftrightarrow (\neg φ \land \neg ψ)$
3		df-3or	$⊢ (φ \lor ψ \lor χ) \leftrightarrow ((φ \lor ψ) \lor χ)$
4	1 3	mpbi	$⊢ ((φ \lor ψ) \lor χ)$
5	4	ori	$⊢ \neg (φ \lor ψ) \to χ$
6	2 5	sylbir	$⊢ (\neg φ \land \neg ψ) \to χ$