Theorem iinab 4391

Description: Indexed intersection of a class builder. (Contributed by NM, 6-Dec-2011.)

Assertion

Ref	Expression
iinab

Distinct variable groups:   ,   ,

Proof of Theorem iinab

Step	Hyp	Ref	Expression
1		nfcv 2619	. . . 4
2		nfab1 2621	. . . 4
3	1, 2	nfiin 4359	. . 3
4		nfab1 2621	. . 3
5	3, 4	cleqf 2646	. 2
6		abid 2444	. . . 4
7	6	ralbii 2888	. . 3
8		vex 3112	. . . 4
9		eliin 4336	. . . 4
10	8, 9	ax-mp 5	. . 3
11		abid 2444	. . 3
12	7, 10, 11	3bitr4i 277	. 2
13	5, 12	mpgbir 1622	1

Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  cvv 3109  |^|_ciin 4331

This theorem is referenced by:  iinrab  4392

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-v 3111  df-iin 4333