Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  orcs Structured version   Unicode version

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
Assertion
Ref Expression
orcs

Proof of Theorem orcs
StepHypRef Expression
1 orc 376 . 2
2 orcs.1 . 2
31, 2syl 16 1
 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
 Copyright terms: Public domain W3C validator