ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orass Unicode version

Theorem orass 739
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 700 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ch  \/  ( ph  \/  ps ) ) )
2 or12 738 . 2  |-  ( ( ch  \/  ( ph  \/  ps ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 orcom 700 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
43orbi2i 734 . 2  |-  ( (
ph  \/  ( ch  \/  ps ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
51, 2, 43bitri 205 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 680
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm2.31  740  pm2.32  741  or32  742  or4  743  3orass  948  dveeq2  1769  dveeq2or  1770  sbequilem  1792  dvelimALT  1961  dvelimfv  1962  dvelimor  1969  unass  3201  ltxr  9513  lcmass  11673
  Copyright terms: Public domain W3C validator