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Theorem eusvnfb 4132
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 4131 . . 3  F/_
2 euex 1908 . . . 4
3 id 19 . . . . . . 7
4 vex 2534 . . . . . . 7 
_V
53, 4syl6eqelr 2107 . . . . . 6  _V
65sps 1408 . . . . 5  _V
76exlimiv 1467 . . . 4  _V
82, 7syl 14 . . 3  _V
91, 8jca 290 . 2  F/_  _V
10 isset 2535 . . . . 5  _V
11 nfcvd 2157 . . . . . . . 8  F/_  F/_
12 id 19 . . . . . . . 8  F/_  F/_
1311, 12nfeqd 2170 . . . . . . 7  F/_  F/
1413nfrd 1390 . . . . . 6  F/_
1514eximdv 1738 . . . . 5  F/_
1610, 15syl5bi 141 . . . 4  F/_  _V
1716imp 115 . . 3 
F/_  _V
18 eusv1 4130 . . 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 1224   wceq 1226  wex 1358   wcel 1370  weu 1878   F/_wnfc 2143   _Vcvv 2531
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-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-eu 1881  df-mo 1882  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-sbc 2738  df-csb 2826
This theorem is referenced by:  eusv2nf  4134  eusv2  4135
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