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Theorem eltpi 4031
Description: A member of an unordered triple of classes is one of them. (Contributed by Mario Carneiro, 11-Feb-2015.)
Assertion
Ref Expression
eltpi  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  =  B  \/  A  =  C  \/  A  =  D ) )

Proof of Theorem eltpi
StepHypRef Expression
1 eltpg 4029 . 2  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  e.  { B ,  C ,  D }  <->  ( A  =  B  \/  A  =  C  \/  A  =  D ) ) )
21ibi 241 1  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  =  B  \/  A  =  C  \/  A  =  D ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ w3o 964    = wceq 1370    e. wcel 1758   {ctp 3992
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3080  df-un 3444  df-sn 3989  df-pr 3991  df-tp 3993
This theorem is referenced by:  perfectlem2  22705  sgnmulsgn  27096  sgnmulsgp  27097  kur14lem7  27264
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