Theorem inrab2 3770

Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.)

Assertion

Ref	Expression
inrab2

Distinct variable group:   ,

Proof of Theorem inrab2

Step	Hyp	Ref	Expression
1		df-rab 2816	. . 3
2		abid2 2597	. . . 4
3	2	eqcomi 2470	. . 3
4	1, 3	ineq12i 3697	. 2
5		df-rab 2816	. . 3
6		inab 3765	. . . 4
7		elin 3686	. . . . . . 7
8	7	anbi1i 695	. . . . . 6
9		an32 798	. . . . . 6
10	8, 9	bitri 249	. . . . 5
11	10	abbii 2591	. . . 4
12	6, 11	eqtr4i 2489	. . 3
13	5, 12	eqtr4i 2489	. 2
14	4, 13	eqtr4i 2489	1

Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  i^icin 3474

This theorem is referenced by:  iooval2  11591  fzval2  11704  smuval2  14132  smueqlem  14140  dfphi2  14304  ordtrest  19703  ordtrest2lem  19704  ordtrestNEW  27903  ordtrest2NEWlem  27904  itg2addnclem2  30067  dmatALTbas  33002

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-rab 2816  df-v 3111  df-in 3482