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Theorem iunab 4317
 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 2564 . . . 4
2 nfab1 2566 . . . 4
31, 2nfiun 4299 . . 3
4 nfab1 2566 . . 3
53, 4cleqf 2591 . 2
6 abid 2389 . . . 4
76rexbii 2906 . . 3
8 eliun 4276 . . 3
9 abid 2389 . . 3
107, 8, 93bitr4i 277 . 2
115, 10mpgbir 1643 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1405   wcel 1842  cab 2387  wrex 2755  ciun 4271 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rex 2760  df-v 3061  df-iun 4273 This theorem is referenced by:  iunrab  4318  iunid  4326  dfimafn2  5899  rabiun  31408  dfaimafn2  37619  rnfdmpr  37941
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