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

Step	Hyp	Ref	Expression
1		nfcv 2619	. . . 4
2		nfab1 2621	. . . 4
3	1, 2	nfiun 4358	. . 3
4		nfab1 2621	. . 3
5	3, 4	cleqf 2646	. 2
6		abid 2444	. . . 4
7	6	rexbii 2959	. . 3
8		eliun 4335	. . 3
9		abid 2444	. . 3
10	7, 8, 9	3bitr4i 277	. 2
11	5, 10	mpgbir 1622	1

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