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Metamath Proof Explorer

Theorem olcs

Description: Deduction eliminating disjunct. (Contributed by NM, 21-Jun-1994) (Proof shortened by Wolf Lammen, 3-Oct-2013)

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

Step	Hyp	Ref	Expression
1		olcs.1	$⊢ (φ \lor ψ) \to χ$
2	1	orcoms	$⊢ (ψ \lor φ) \to χ$
3	2	orcs	$⊢ ψ \to χ$