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Theorem dftp2 3620
Description: Alternate definition of unordered triple of classes. Special case of Definition 5.3 of [TakeutiZaring] p. 16. (Contributed by NM, 8-Apr-1994.)
Assertion
Ref Expression
dftp2  |-  { A ,  B ,  C }  =  { x  |  ( x  =  A  \/  x  =  B  \/  x  =  C ) }
Distinct variable groups:    x, A    x, B    x, C

Proof of Theorem dftp2
StepHypRef Expression
1 vex 2743 . . 3  |-  x  e. 
_V
21eltp 3619 . 2  |-  ( x  e.  { A ,  B ,  C }  <->  ( x  =  A  \/  x  =  B  \/  x  =  C )
)
32abbi2i 2367 1  |-  { A ,  B ,  C }  =  { x  |  ( x  =  A  \/  x  =  B  \/  x  =  C ) }
Colors of variables: wff set class
Syntax hints:    \/ w3o 938    = wceq 1619   {cab 2242   {ctp 3583
This theorem is referenced by:  tprot  3663  tpid3g  3682  en3lplem2  7350  tpid3gVD  27631  en3lplem2VD  27633
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2742  df-un 3099  df-sn 3587  df-pr 3588  df-tp 3589
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