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Theorem zfpair2 3915
Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 3914. (Contributed by NM, 14-Nov-2006.)
Assertion
Ref Expression
zfpair2  { ,  }  _V

Proof of Theorem zfpair2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-pr 3914 . . . 4
21bm1.3ii 3848 . . 3
3 dfcleq 2012 . . . . 5  { ,  }  { ,  }
4 vex 2534 . . . . . . . 8 
_V
54elpr 3364 . . . . . . 7  { ,  }
65bibi2i 216 . . . . . 6 
{ ,  }
76albii 1335 . . . . 5  { ,  }
83, 7bitri 173 . . . 4  { ,  }
98exbii 1474 . . 3  { ,  }
102, 9mpbir 134 . 2  { ,  }
1110issetri 2538 1  { ,  }  _V
Colors of variables: wff set class
Syntax hints:   wb 98   wo 616  wal 1224   wceq 1226  wex 1358   wcel 1370   _Vcvv 2531   {cpr 3347
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-14 1382  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000  ax-sep 3845  ax-pr 3914
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-un 2895  df-sn 3352  df-pr 3353
This theorem is referenced by:  prexgOLD  3916  prexg  3917  funopg  4856
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