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Theorem iunun 4163
 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 2855 . . . 4
2 elun 3480 . . . . 5
32rexbii 2722 . . . 4
4 eliun 4089 . . . . 5
5 eliun 4089 . . . . 5
64, 5orbi12i 508 . . . 4
71, 3, 63bitr4i 269 . . 3
8 eliun 4089 . . 3
9 elun 3480 . . 3
107, 8, 93bitr4i 269 . 2
1110eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1652   wcel 1725  wrex 2698   cun 3310  ciun 4085 This theorem is referenced by:  iununi  4167  oarec  6797  uniiccdif  19462  dftrpred4g  25504  comppfsc  26378  bnj1415  29344 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-un 3317  df-iun 4087
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