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Theorem 3mix2 1165
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3mix2  |-  ( ph  ->  ( ps  \/  ph  \/  ch ) )

Proof of Theorem 3mix2
StepHypRef Expression
1 3mix1 1164 . 2  |-  ( ph  ->  ( ph  \/  ch  \/  ps ) )
2 3orrot 978 . 2  |-  ( ( ps  \/  ph  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )
31, 2sylibr 212 1  |-  ( ph  ->  ( ps  \/  ph  \/  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ w3o 971
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-3or 973
This theorem is referenced by:  3mix2i  1168  3mix2d  1171  3jaob  1289  tppreqb  4153  onzsl  6663  sornom  8657  hash1to3  12506  cshwshashlem1  14454  ostth  23693  sltsolem1  29400  nodenselem8  29420  fnwe2lem3  30970  tpres  32390  nn0le2is012  32684
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