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Theorem eusvnfb 4648
 Description: Two ways to say that A(x) is a set expression that does not depend on . (Contributed by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
eusvnfb
Distinct variable groups:   ,   ,

Proof of Theorem eusvnfb
StepHypRef Expression
1 eusvnf 4647 . . 3
2 euex 2308 . . . 4
3 eqvisset 3117 . . . . . 6
43sps 1865 . . . . 5
54exlimiv 1722 . . . 4
62, 5syl 16 . . 3
71, 6jca 532 . 2
8 isset 3113 . . . . 5
9 nfcvd 2620 . . . . . . . 8
10 id 22 . . . . . . . 8
119, 10nfeqd 2626 . . . . . . 7
1211nfrd 1875 . . . . . 6
1312eximdv 1710 . . . . 5
148, 13syl5bi 217 . . . 4
1514imp 429 . . 3
16 eusv1 4646 . . 3
1715, 16sylibr 212 . 2
187, 17impbii 188 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282  F/_wnfc 2605   cvv 3109 This theorem is referenced by:  eusv2nf  4650  eusv2  4651 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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