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Theorem eltpi 3690
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 3689 . 2  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  e.  { B ,  C ,  D }  <->  ( A  =  B  \/  A  =  C  \/  A  =  D ) ) )
21ibi 232 1  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  =  B  \/  A  =  C  \/  A  =  D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ w3o 933    = wceq 1632    e. wcel 1696   {ctp 3655
This theorem is referenced by:  perfectlem2  20485  kur14lem7  23758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660  df-tp 3661
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