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Theorem iunun 3775
 Description: Separate a union in an indexed union. (Contributed by NM, 27-Dec-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iunun

Proof of Theorem iunun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 r19.43 2517 . . . 4
2 elun 3123 . . . . 5
32rexbii 2378 . . . 4
4 eliun 3702 . . . . 5
5 eliun 3702 . . . . 5
64, 5orbi12i 714 . . . 4
71, 3, 63bitr4i 210 . . 3
8 eliun 3702 . . 3
9 elun 3123 . . 3
107, 8, 93bitr4i 210 . 2
1110eqriv 2080 1
 Colors of variables: wff set class Syntax hints:   wo 662   wceq 1285   wcel 1434  wrex 2354   cun 2980  ciun 3698 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 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2986  df-iun 3700 This theorem is referenced by: (None)
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