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Theorem 3mix3 1333
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3mix3 (𝜑 → (𝜓𝜒𝜑))

Proof of Theorem 3mix3
StepHypRef Expression
1 3mix1 1331 . 2 (𝜑 → (𝜑𝜓𝜒))
2 3orrot 1092 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
31, 2sylib 218 1 (𝜑 → (𝜓𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3o 1086
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 207  df-or 849  df-3or 1088
This theorem is referenced by:  3mix3i  1336  3mix3d  1339  3jaobOLD  1429  tppreqb  4805  tpres  7221  onzsl  7867  sornom  10317  fpwwe2lem12  10682  nn0le2is012  12682  nn01to3  12983  qbtwnxr  13242  hash1to3  14531  swrdnd0  14695  pfxnd  14725  cshwshashlem1  17133  ostth  27683  nolesgn2o  27716  sltsolem1  27720  nosep2o  27727  btwncolinear1  36070  tpid3gVD  44862  limcicciooub  45652  dfxlim2v  45862
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