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Theorem orass 526
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 388 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ch  \/  ( ph  \/  ps ) ) )
2 or12 525 . 2  |-  ( ( ch  \/  ( ph  \/  ps ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 orcom 388 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
43orbi2i 521 . 2  |-  ( (
ph  \/  ( ch  \/  ps ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
51, 2, 43bitri 274 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    \/ wo 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371
This theorem is referenced by:  pm2.31  527  pm2.32  528  or32  529  or4  530  3orass  985  axi12  2406  unass  3566  tppreqb  4084  ltxr  11366  lcmass  14522  plydivex  23192  disjxpin  28144  impor  32221  ifpim123g  36057
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