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Theorem iunun 4411
 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 3013 . . . 4
2 elun 3644 . . . . 5
32rexbii 2959 . . . 4
4 eliun 4335 . . . . 5
5 eliun 4335 . . . . 5
64, 5orbi12i 521 . . . 4
71, 3, 63bitr4i 277 . . 3
8 eliun 4335 . . 3
9 elun 3644 . . 3
107, 8, 93bitr4i 277 . 2
1110eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  \/wo 368  =wceq 1395  e.wcel 1818  E.wrex 2808  u.cun 3473  U_ciun 4330 This theorem is referenced by:  iununi  4415  oarec  7230  comppfsc  20033  uniiccdif  21987  dftrpred4g  29317  bnj1415  34094 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-or 370  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-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-un 3480  df-iun 4332
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