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Theorem bj-zfpair2 7133
Description: Proof of zfpair2 3919 using only bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-zfpair2  { ,  }  _V

Proof of Theorem bj-zfpair2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-bdeq 7047 . . . . 5 BOUNDED
2 ax-bdeq 7047 . . . . 5 BOUNDED
31, 2ax-bdor 7043 . . . 4 BOUNDED
4 ax-pr 3918 . . . 4
53, 4bdbm1.3ii 7117 . . 3
6 dfcleq 2016 . . . . 5  { ,  }  { ,  }
7 vex 2538 . . . . . . . 8 
_V
87elpr 3368 . . . . . . 7  { ,  }
98bibi2i 216 . . . . . 6 
{ ,  }
109albii 1339 . . . . 5  { ,  }
116, 10bitri 173 . . . 4  { ,  }
1211exbii 1478 . . 3  { ,  }
135, 12mpbir 134 . 2  { ,  }
1413issetri 2542 1  { ,  }  _V
Colors of variables: wff set class
Syntax hints:   wb 98   wo 616  wal 1226   wceq 1228  wex 1362   wcel 1374   _Vcvv 2535   {cpr 3351
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-pr 3918  ax-bdor 7043  ax-bdeq 7047  ax-bdsep 7111
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899  df-sn 3356  df-pr 3357
This theorem is referenced by:  bj-prexg  7134
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