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Theorem 3orrot 930
Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3orrot  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ch  \/  ph ) )

Proof of Theorem 3orrot
StepHypRef Expression
1 orcom 682 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ( ps  \/  ch )  \/ 
ph ) )
2 3orass 927 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 df-3or 925 . 2  |-  ( ( ps  \/  ch  \/  ph )  <->  ( ( ps  \/  ch )  \/ 
ph ) )
41, 2, 33bitr4i 210 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ch  \/  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 664    \/ w3o 923
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115  df-3or 925
This theorem is referenced by:  3mix2  1113  3mix3  1114  eueq3dc  2789  tprot  3535  sotritrieq  4152  elnnz  8760  elznn  8766  ztri3or0  8792  zapne  8821
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