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Theorem dftp2 4040
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 3081 . . 3  |-  x  e. 
_V
21eltp 4039 . 2  |-  ( x  e.  { A ,  B ,  C }  <->  ( x  =  A  \/  x  =  B  \/  x  =  C )
)
32abbi2i 2553 1  |-  { A ,  B ,  C }  =  { x  |  ( x  =  A  \/  x  =  B  \/  x  =  C ) }
Colors of variables: wff setvar class
Syntax hints:    \/ w3o 981    = wceq 1437   {cab 2405   {ctp 3997
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-v 3080  df-un 3438  df-sn 3994  df-pr 3996  df-tp 3998
This theorem is referenced by:  tprot  4089  tpid3g  4109  en3lplem2  8111  tpid3gVD  36911  en3lplem2VD  36913
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