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Metamath Proof Explorer

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	\|- ( ( ph \/ ps ) -> ch )
	Assertion	orcs	\|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		orcs.1	\|- ( ( ph \/ ps ) -> ch )
2		orc	\|- ( ph -> ( ph \/ ps ) )
3	2 1	syl	\|- ( ph -> ch )