Theorem elintab 4297

Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993.)

Hypothesis

Ref	Expression
inteqab.1

Assertion

Ref	Expression
elintab

Distinct variable group:   ,

Proof of Theorem elintab

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		inteqab.1	. . 3
2	1	elint 4292	. 2
3		nfsab1 2446	. . . 4
4		nfv 1707	. . . 4
5	3, 4	nfim 1920	. . 3
6		nfv 1707	. . 3
7		eleq1 2529	. . . . 5
8		abid 2444	. . . . 5
9	7, 8	syl6bb 261	. . . 4
10		eleq2 2530	. . . 4
11	9, 10	imbi12d 320	. . 3
12	5, 6, 11	cbval 2021	. 2
13	2, 12	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  {cab 2442  cvv 3109  |^|cint 4286

This theorem is referenced by:  elintrab  4298  intmin4  4316  intab  4317  intid  4710  dfom3  8085  dfom5  8088  tc2  8194  dfnn2  10574  efgi  16737  efgi2  16743  mclsax  28929  heibor1lem  30305  brintclab  37763

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-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-v 3111  df-int 4287