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Theorem eusvnfb 4721
 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
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusvnfb
StepHypRef Expression
1 eusvnf 4720 . . 3
2 euex 2306 . . . 4
3 id 21 . . . . . . 7
4 vex 2961 . . . . . . 7
53, 4syl6eqelr 2527 . . . . . 6
65sps 1771 . . . . 5
76exlimiv 1645 . . . 4
82, 7syl 16 . . 3
91, 8jca 520 . 2
10 isset 2962 . . . . 5
11 nfcvd 2575 . . . . . . . 8
12 id 21 . . . . . . . 8
1311, 12nfeqd 2588 . . . . . . 7
1413nfrd 1780 . . . . . 6
1514eximdv 1633 . . . . 5
1610, 15syl5bi 210 . . . 4
1716imp 420 . . 3
18 eusv1 4719 . . 3
1917, 18sylibr 205 . 2
209, 19impbii 182 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1726  weu 2283  wnfc 2561  cvv 2958 This theorem is referenced by:  eusv2nf  4723  eusv2  4724 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-csb 3254
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