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Theorem iunab 4137
 Description: The indexed union of a class abstraction. (Contributed by NM, 27-Dec-2004.)
Assertion
Ref Expression
iunab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem iunab
StepHypRef Expression
1 nfcv 2572 . . . 4
2 nfab1 2574 . . . 4
31, 2nfiun 4119 . . 3
4 nfab1 2574 . . 3
53, 4cleqf 2596 . 2
6 abid 2424 . . . 4
76rexbii 2730 . . 3
8 eliun 4097 . . 3
9 abid 2424 . . 3
107, 8, 93bitr4i 269 . 2
115, 10mpgbir 1559 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cab 2422  wrex 2706  ciun 4093 This theorem is referenced by:  iunrab  4138  iunid  4146  dfimafn2  5776  rabiun  26236  dfaimafn2  28006  rnfdmpr  28083 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-iun 4095
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