Theorem iinrab 4392

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

Assertion

Ref	Expression
iinrab

Distinct variable groups:   ,,   ,

Proof of Theorem iinrab

Step	Hyp	Ref	Expression
1		r19.28zv 3924	. . 3
2	1	abbidv 2593	. 2
3		df-rab 2816	. . . . 5
4	3	a1i 11	. . . 4
5	4	iineq2i 4350	. . 3
6		iinab 4391	. . 3
7	5, 6	eqtri 2486	. 2
8		df-rab 2816	. 2
9	2, 7, 8	3eqtr4g 2523	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  =/=wne 2652  A.wral 2807  {crab 2811  c0 3784  |^|_ciin 4331

This theorem is referenced by:  iinrab2  4393  riinrab  4406  ubthlem1  25786  pmapglbx  35493

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-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-nul 3785  df-iin 4333