Theorem orcs

Description: Deduction eliminating disjunct.Notational convention: We sometimes suffix with "s" the label of an inference that manipulates an antecedent, leaving the consequent unchanged. The "s" means that the inference eliminates the need for a syllogism ( syl ) -type inference in a proof. (Contributed by NM, 21-Jun-1994)

	Ref	Expression
Hypothesis	orcs.1	$$⊢\left(\phi \vee \psi \right)\to \chi$$
Assertion	orcs	$$⊢\phi \to \chi$$

Proof

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