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Theorem orcs 654
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 14) -type inference in a proof. (Contributed by NM, 21-Jun-1994.)
Ref Expression
orcs.1 ((𝜑𝜓) → 𝜒)
Ref Expression
orcs (𝜑𝜒)

Proof of Theorem orcs
StepHypRef Expression
1 orc 633 . 2 (𝜑 → (𝜑𝜓))
2 orcs.1 . 2 ((𝜑𝜓) → 𝜒)
31, 2syl 14 1 (𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  olcs  655
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