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Theorem elunii 3585
 Description: Membership in class union. (Contributed by NM, 24-Mar-1995.)
Assertion
Ref Expression
elunii

Proof of Theorem elunii
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2101 . . . . 5
2 eleq1 2100 . . . . 5
31, 2anbi12d 442 . . . 4
43spcegv 2641 . . 3
54anabsi7 515 . 2
6 eluni 3583 . 2
75, 6sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wcel 1393  cuni 3580 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-uni 3581 This theorem is referenced by:  ssuni  3602  unipw  3953  opeluu  4182  sucunielr  4236  unon  4237  ordunisuc2r  4240  tfrlemibxssdm  5941
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