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Theorem orass 512
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 378 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ch  \/  ( ph  \/  ps ) ) )
2 or12 511 . 2  |-  ( ( ch  \/  ( ph  \/  ps ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 orcom 378 . . 3  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
43orbi2i 507 . 2  |-  ( (
ph  \/  ( ch  \/  ps ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
51, 2, 43bitri 264 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  (
ph  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359
This theorem is referenced by:  pm2.31  513  pm2.32  514  or32  515  or4  516  3orass  942  unass  3242  ltxr  10336  plydivex  19509
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
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