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Theorem euabex 3935
Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
euabex  {  |  }  _V

Proof of Theorem euabex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euabsn2 3413 . 2  {  |  }  { }
2 vex 2538 . . . . 5 
_V
3 snexgOLD 3909 . . . . 5  _V  { }  _V
42, 3ax-mp 7 . . . 4  { }  _V
5 eleq1 2082 . . . 4  {  |  }  { }  {  |  }  _V  { }  _V
64, 5mpbiri 157 . . 3  {  |  }  { }  {  |  }  _V
76exlimiv 1471 . 2  {  |  }  { }  {  |  }  _V
81, 7sylbi 114 1  {  |  }  _V
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1228  wex 1362   wcel 1374  weu 1882   {cab 2008   _Vcvv 2535   {csn 3350
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-sep 3849  ax-pow 3901
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-in 2901  df-ss 2908  df-pw 3336  df-sn 3356
This theorem is referenced by: (None)
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