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Theorem iunxun 3892
 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 3256 . . . 4
2 eliun 3817 . . . . 5
3 eliun 3817 . . . . 5
42, 3orbi12i 753 . . . 4
51, 4bitr4i 186 . . 3
6 eliun 3817 . . 3
7 elun 3217 . . 3
85, 6, 73bitr4i 211 . 2
98eqriv 2136 1
 Colors of variables: wff set class Syntax hints:   wo 697   wceq 1331   wcel 1480  wrex 2417   cun 3069  ciun 3813 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-iun 3815 This theorem is referenced by:  iunxprg  3893  iunsuc  4342  rdgisuc1  6281  oasuc  6360  omsuc  6368  iunfidisj  6834  fsum2dlemstep  11210  fsumiun  11253  iuncld  12294
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