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Theorem dftp2 3630
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 2733 . . 3  |-  x  e. 
_V
21eltp 3629 . 2  |-  ( x  e.  { A ,  B ,  C }  <->  ( x  =  A  \/  x  =  B  \/  x  =  C )
)
32abbi2i 2285 1  |-  { A ,  B ,  C }  =  { x  |  ( x  =  A  \/  x  =  B  \/  x  =  C ) }
Colors of variables: wff set class
Syntax hints:    \/ w3o 972    = wceq 1348   {cab 2156   {ctp 3583
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3or 974  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-sn 3587  df-pr 3588  df-tp 3589
This theorem is referenced by:  tprot  3674  tpid3g  3696
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