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Theorem orass 531
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 393 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ch  \/  ( ph  \/  ps ) ) )
2 or12 530 . 2  |-  ( ( ch  \/  ( ph  \/  ps ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 orcom 393 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
43orbi2i 526 . 2  |-  ( (
ph  \/  ( ch  \/  ps ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
51, 2, 43bitri 279 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    \/ wo 374
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 190  df-or 376
This theorem is referenced by:  pm2.31  532  pm2.32  533  or32  534  or4  535  3orass  994  axi12  2440  unass  3603  tppreqb  4126  ltxr  11449  lcmass  14634  plydivex  23306  disjxpin  28252  impor  32360  ifpim123g  36190
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