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Theorem 3orcomb 971
Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 717 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
21orbi2i 751 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 3orass 965 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
4 3orass 965 . 2  |-  ( (
ph  \/  ch  \/  ps )  <->  ( ph  \/  ( ch  \/  ps ) ) )
52, 3, 43bitr4i 211 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 697    \/ w3o 961
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 698
This theorem depends on definitions:  df-bi 116  df-3or 963
This theorem is referenced by:  eueq3dc  2853  sotritrieq  4242
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