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	$$⊢\left(\phi \vee \psi \right)\to \chi$$
Assertion	olcs	$$⊢\psi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		olcs.1	$$⊢\left(\phi \vee \psi \right)\to \chi$$
2	1	orcoms	$$⊢\left(\psi \vee \phi \right)\to \chi$$
3	2	orcs	$$⊢\psi \to \chi$$