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Theorem or12 510
Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)
Assertion
Ref Expression
or12  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )

Proof of Theorem or12
StepHypRef Expression
1 pm1.5 509 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )
2 pm1.5 509 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  -> 
( ph  \/  ( ps  \/  ch ) ) )
31, 2impbii 181 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358
This theorem is referenced by:  orass  511  or32  514  or4  515  3orcoma  944  sotrieq  4522  ordzsl  4817  plydivex  20206  socnv  25380
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
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