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

Theorem orabs 831
Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 28-Feb-2014.)
Assertion
Ref Expression
orabs  |-  ( ph  <->  ( ( ph  \/  ps )  /\  ph ) )

Proof of Theorem orabs
StepHypRef Expression
1 orc 376 . 2  |-  ( ph  ->  ( ph  \/  ps ) )
21pm4.71ri 617 1  |-  ( ph  <->  ( ( ph  \/  ps )  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
  Copyright terms: Public domain W3C validator