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

Theorem orass 511
Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
orass  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )

Proof of Theorem orass
StepHypRef Expression
1 orcom 377 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ch  \/  ( ph  \/  ps ) ) )
2 or12 510 . 2  |-  ( ( ch  \/  ( ph  \/  ps ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 orcom 377 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
43orbi2i 506 . 2  |-  ( (
ph  \/  ( ch  \/  ps ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
51, 2, 43bitri 263 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358
This theorem is referenced by:  pm2.31  512  pm2.32  513  or32  514  or4  515  jaoi2  934  3orass  939  axi12  2383  unass  3464  tppreqb  3899  ltxr  10671  plydivex  20167  disjxpin  23981
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 178  df-or 360
  Copyright terms: Public domain W3C validator