Theorem orcs 383

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 15) -type inference in a proof. (Contributed by NM, 21-Jun-1994.)

Hypothesis

Ref	Expression
orcs.1	⊢ ((φ ∨ ψ) → χ)

Assertion

Ref	Expression
orcs	⊢ (φ → χ)

Proof of Theorem orcs

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ ψ))
2		orcs.1	. 2 ⊢ ((φ ∨ ψ) → χ)
3	1, 2	syl 15	1 ⊢ (φ → χ)

Syntax hints:   → wi 4   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  olcs  384  ifor  3703