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Theorem eusvnfb 4595
 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 4594 . . 3
2 euex 2290 . . . 4
3 eqvisset 3084 . . . . . 6
43sps 1805 . . . . 5
54exlimiv 1689 . . . 4
62, 5syl 16 . . 3
71, 6jca 532 . 2
8 isset 3080 . . . . 5
9 nfcvd 2617 . . . . . . . 8
10 id 22 . . . . . . . 8
119, 10nfeqd 2623 . . . . . . 7
1211nfrd 1814 . . . . . 6
1312eximdv 1677 . . . . 5
148, 13syl5bi 217 . . . 4
1514imp 429 . . 3
16 eusv1 4593 . . 3
1715, 16sylibr 212 . 2
187, 17impbii 188 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369  wal 1368   wceq 1370  wex 1587   wcel 1758  weu 2262  wnfc 2602  cvv 3076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-fal 1376  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3078  df-sbc 3293  df-csb 3395  df-dif 3438  df-in 3442  df-ss 3449  df-nul 3745 This theorem is referenced by:  eusv2nf  4597  eusv2  4598
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