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Theorem orcs 392
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 17) -type inference in a proof. (Contributed by NM, 21-Jun-1994.)
Hypothesis
Ref Expression
orcs.1  |-  ( (
ph  \/  ps )  ->  ch )
Assertion
Ref Expression
orcs  |-  ( ph  ->  ch )

Proof of Theorem orcs
StepHypRef Expression
1 orc 383 . 2  |-  ( ph  ->  ( ph  \/  ps ) )
2 orcs.1 . 2  |-  ( (
ph  \/  ps )  ->  ch )
31, 2syl 17 1  |-  ( ph  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 366
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 185  df-or 368
This theorem is referenced by:  olcs  393  ifor  3931  tppreqb  4112  frxp  6893  mndifsplit  19428  maducoeval2  19432  leibpilem2  23595  leibpi  23596  3o1cs  27768  3o2cs  27769  tsan2  31811  frege114d  35717
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