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Theorem elunii 3614
 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 2143 . . . . 5
2 eleq1 2142 . . . . 5
31, 2anbi12d 457 . . . 4
43spcegv 2687 . . 3
54anabsi7 546 . 2
6 eluni 3612 . 2
75, 6sylibr 132 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285  wex 1422   wcel 1434  cuni 3609 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-uni 3610 This theorem is referenced by:  ssuni  3631  unipw  3980  opeluu  4208  sucunielr  4262  unon  4263  ordunisuc2r  4266  tfrlemibxssdm  5976  tfr1onlemsucaccv  5990  tfr1onlembxssdm  5992  tfrcllemsucaccv  6003  tfrcllembxssdm  6005
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