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Theorem orcs 385
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 16) -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 376 . 2  |-  ( ph  ->  ( ph  \/  ps ) )
2 orcs.1 . 2  |-  ( (
ph  \/  ps )  ->  ch )
31, 2syl 16 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 359
This theorem is referenced by:  olcs  386  ifor  3781  tppreqb  3941  frxp  6458  leibpilem2  20783  leibpi  20784  3o1cs  23955  3o2cs  23956
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-or 361
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