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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	⊢ ( ( 𝜑 ∨ 𝜓 ) → 𝜒 )
	Assertion	orcs	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		orcs.1	⊢ ( ( 𝜑 ∨ 𝜓 ) → 𝜒 )
2		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
3	2 1	syl	⊢ ( 𝜑 → 𝜒 )