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Theorem iunxun 4174
 Description: Separate a union in the index of an indexed union. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iunxun

Proof of Theorem iunxun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rexun 3529 . . . 4
2 eliun 4099 . . . . 5
3 eliun 4099 . . . . 5
42, 3orbi12i 509 . . . 4
51, 4bitr4i 245 . . 3
6 eliun 4099 . . 3
7 elun 3490 . . 3
85, 6, 73bitr4i 270 . 2
98eqriv 2435 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1653   wcel 1726  wrex 2708   cun 3320  ciun 4095 This theorem is referenced by:  iunsuc  4665  funiunfv  5997  iunfi  7396  kmlem11  8042  ackbij1lem9  8110  fsum2dlem  12556  fsumiun  12602  prmreclem4  13289  fiuncmp  17469  ovolfiniun  19399  finiunmbl  19440  volfiniun  19443  voliunlem1  19446  uniioombllem4  19480  iuninc  24013  indval2  24414  sigaclfu2  24506  measvuni  24570  sibfof  24656  cvmliftlem10  24983  fprod2dlem  25306  mblfinlem2  26246  iunxprg  28070 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-un 3327  df-iun 4097
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