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Theorem eusvnfb 4152
Description: Two ways to say that is a set expression that does not depend on . (Contributed by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
eusvnfb  F/_  _V
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusvnfb
StepHypRef Expression
1 eusvnf 4151 . . 3  F/_
2 euex 1927 . . . 4
3 id 19 . . . . . . 7
4 vex 2554 . . . . . . 7 
_V
53, 4syl6eqelr 2126 . . . . . 6  _V
65sps 1427 . . . . 5  _V
76exlimiv 1486 . . . 4  _V
82, 7syl 14 . . 3  _V
91, 8jca 290 . 2  F/_  _V
10 isset 2555 . . . . 5  _V
11 nfcvd 2176 . . . . . . . 8  F/_  F/_
12 id 19 . . . . . . . 8  F/_  F/_
1311, 12nfeqd 2189 . . . . . . 7  F/_  F/
1413nfrd 1410 . . . . . 6  F/_
1514eximdv 1757 . . . . 5  F/_
1610, 15syl5bi 141 . . . 4  F/_  _V
1716imp 115 . . 3 
F/_  _V
18 eusv1 4150 . . 3
1917, 18sylibr 137 . 2 
F/_  _V
209, 19impbii 117 1  F/_  _V
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390  weu 1897   F/_wnfc 2162   _Vcvv 2551
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-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-csb 2847
This theorem is referenced by:  eusv2nf  4154  eusv2  4155
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