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Theorem 3mix1d 1169
Description: Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)
Hypothesis
Ref Expression
3mixd.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
3mix1d  |-  ( ph  ->  ( ps  \/  ch  \/  th ) )

Proof of Theorem 3mix1d
StepHypRef Expression
1 3mixd.1 . 2  |-  ( ph  ->  ps )
2 3mix1 1163 . 2  |-  ( ps 
->  ( ps  \/  ch  \/  th ) )
31, 2syl 16 1  |-  ( ph  ->  ( ps  \/  ch  \/  th ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ w3o 970
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 368  df-3or 972
This theorem is referenced by:  f1dom3fv3dif  6150  f1dom3el3dif  6151  elfiun  7882  estrreslem2  15609  ostth  24025  btwncolg1  24146  hlln  24195  btwnlng1  24203  sltsolem1  29671  nodense  29692  colineartriv1  29948  fnwe2lem3  31240
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