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Theorem eltpi 4044
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 4042 . 2  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  e.  { B ,  C ,  D }  <->  ( A  =  B  \/  A  =  C  \/  A  =  D ) ) )
21ibi 244 1  |-  ( A  e.  { B ,  C ,  D }  ->  ( A  =  B  \/  A  =  C  \/  A  =  D ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ w3o 981    = wceq 1437    e. wcel 1872   {ctp 4002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082  df-un 3441  df-sn 3999  df-pr 4001  df-tp 4003
This theorem is referenced by:  perfectlem2  24156  sgnmulsgn  29428  sgnmulsgp  29429  kur14lem7  29943  perfectALTVlem2  38714
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