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Theorem or12 740
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 pm1.5 739 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )
2 pm1.5 739 . 2  |-  ( ( ps  \/  ( ph  \/  ch ) )  -> 
( ph  \/  ( ps  \/  ch ) ) )
31, 2impbii 125 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ps  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 682
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 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  orass  741  or32  744  or4  745
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