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Theorem iunab 4376
 Description: The indexed union of a class abstraction. (Contributed by NM, 27-Dec-2004.)
Assertion
Ref Expression
iunab
Distinct variable groups:   ,   ,

Proof of Theorem iunab
StepHypRef Expression
1 nfcv 2619 . . . 4
2 nfab1 2621 . . . 4
31, 2nfiun 4358 . . 3
4 nfab1 2621 . . 3
53, 4cleqf 2646 . 2
6 abid 2444 . . . 4
76rexbii 2959 . . 3
8 eliun 4335 . . 3
9 abid 2444 . . 3
107, 8, 93bitr4i 277 . 2
115, 10mpgbir 1622 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808  U_ciun 4330 This theorem is referenced by:  iunrab  4377  iunid  4385  dfimafn2  5923  rabiun  30036  dfaimafn2  32251  rnfdmpr  32308 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-iun 4332
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