Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-zfpair2 Structured version   Unicode version

Theorem bj-zfpair2 9365
Description: Proof of zfpair2 3936 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 9275 . . . . 5 BOUNDED
2 ax-bdeq 9275 . . . . 5 BOUNDED
31, 2ax-bdor 9271 . . . 4 BOUNDED
4 ax-pr 3935 . . . 4
53, 4bdbm1.3ii 9346 . . 3
6 dfcleq 2031 . . . . 5  { ,  }  { ,  }
7 vex 2554 . . . . . . . 8 
_V
87elpr 3385 . . . . . . 7  { ,  }
98bibi2i 216 . . . . . 6 
{ ,  }
109albii 1356 . . . . 5  { ,  }
116, 10bitri 173 . . . 4  { ,  }
1211exbii 1493 . . 3  { ,  }
135, 12mpbir 134 . 2  { ,  }
1413issetri 2558 1  { ,  }  _V
Colors of variables: wff set class
Syntax hints:   wb 98   wo 628  wal 1240   wceq 1242  wex 1378   wcel 1390   _Vcvv 2551   {cpr 3368
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-pr 3935  ax-bdor 9271  ax-bdeq 9275  ax-bdsep 9339
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374
This theorem is referenced by:  bj-prexg  9366
  Copyright terms: Public domain W3C validator