Theorem elintrab 4298

Description: Membership in the intersection of a class abstraction. (Contributed by NM, 17-Oct-1999.)

Hypothesis

Ref	Expression
inteqab.1

Assertion

Ref	Expression
elintrab

Distinct variable group:   ,

Proof of Theorem elintrab

Step	Hyp	Ref	Expression
1		inteqab.1	. . . 4
2	1	elintab 4297	. . 3
3		impexp 446	. . . 4
4	3	albii 1640	. . 3
5	2, 4	bitri 249	. 2
6		df-rab 2816	. . . 4
7	6	inteqi 4290	. . 3
8	7	eleq2i 2535	. 2
9		df-ral 2812	. 2
10	5, 8, 9	3bitr4i 277	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  {cab 2442  A.wral 2807  {crab 2811  cvv 3109  |^|cint 4286

This theorem is referenced by:  elintrabg  4299  intmin  4306  rankunb  8289  isf34lem4  8778  ist1-3  19850  filufint  20421  elspani  26461  kur14lem9  28658  lcosslsp  33039  pclclN  35615  elpclN  35616

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-ral 2812  df-rab 2816  df-v 3111  df-int 4287