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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  |-  ( (
ph  \/  ps )  ->  ch )
Assertion
Ref Expression
orcs  |-  ( ph  ->  ch )

Proof of Theorem orcs
StepHypRef Expression
1 orc 374 . 2  |-  ( ph  ->  ( ph  \/  ps ) )
2 orcs.1 . 2  |-  ( (
ph  \/  ps )  ->  ch )
31, 2syl 15 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357
This theorem is referenced by:  olcs  384  ifor  3605  frxp  6225  leibpilem2  20237  leibpi  20238  3o1cs  23097  3o2cs  23098  pnfneige0  23374
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 177  df-or 359
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