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Theorem eluniab 4260
Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
eluniab
Distinct variable group:   ,

Proof of Theorem eluniab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eluni 4252 . 2
2 nfv 1707 . . . 4
3 nfsab1 2446 . . . 4
42, 3nfan 1928 . . 3
5 nfv 1707 . . 3
6 eleq2 2530 . . . 4
7 eleq1 2529 . . . . 5
8 abid 2444 . . . . 5
97, 8syl6bb 261 . . . 4
106, 9anbi12d 710 . . 3
114, 5, 10cbvex 2022 . 2
121, 11bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  {cab 2442  U.cuni 4249
This theorem is referenced by:  elunirab  4261  dfiun2g  4362  inuni  4614  elfv  5869  snnex  6606  unielxp  6836  tfrlem9  7073  dfac5lem2  8526  fin23lem30  8743  unisngl  20028  metrest  21027  aannenlem2  22725  fpwrelmapffslem  27555  wfrlem12  29354  frrlem11  29399  dfiota3  29573
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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-uni 4250
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