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Theorem uniiun 4383
Description: Class union in terms of indexed union. Definition in [Stoll] p. 43. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
uniiun
Distinct variable group:   ,

Proof of Theorem uniiun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfuni2 4251 . 2
2 df-iun 4332 . 2
31, 2eqtr4i 2489 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  {cab 2442  E.wrex 2808  U.cuni 4249  U_ciun 4330
This theorem is referenced by:  iununi  4415  iunpwss  4420  truni  4559  reluni  5130  rnuni  5422  imauni  6158  iunpw  6614  oa0r  7207  om1r  7211  oeworde  7261  unifi  7829  infssuni  7831  cfslb2n  8669  ituniiun  8823  unidom  8939  unictb  8971  gruuni  9199  gruun  9205  hashuni  13638  tgidm  19482  unicld  19547  clsval2  19551  mretopd  19593  tgrest  19660  cmpsublem  19899  cmpsub  19900  tgcmp  19901  hauscmplem  19906  cmpfi  19908  uncon  19930  concompcon  19933  comppfsc  20033  kgentopon  20039  txbasval  20107  txtube  20141  txcmplem1  20142  txcmplem2  20143  xkococnlem  20160  alexsublem  20544  alexsubALT  20551  opnmblALT  22012  limcun  22299  hashunif  27605  dmvlsiga  28129  measinblem  28191  volmeas  28203  cvmscld  28718  istotbnd3  30267  sstotbnd  30271  heiborlem3  30309  heibor  30317
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-rex 2813  df-uni 4250  df-iun 4332
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