Theorem elint2 4293

Description: Membership in class intersection. (Contributed by NM, 14-Oct-1999.)

Hypothesis

Ref	Expression
elint2.1

Assertion

Ref	Expression
elint2

Distinct variable groups:   ,   ,

Proof of Theorem elint2

Step	Hyp	Ref	Expression
1		elint2.1	. . 3
2	1	elint 4292	. 2
3		df-ral 2812	. 2
4	2, 3	bitr4i 252	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  A.wral 2807  cvv 3109  |^|cint 4286

This theorem is referenced by:  elintg  4294  ssint  4302  intssuni  4309  iinuni  4414  trint  4560  trintss  4561  onint  6630  intwun  9134  inttsk  9173  intgru  9213  subgint  16225  subrgint  17451  lssintcl  17610  toponmre  19594  alexsubALTlem3  20549  shintcli  26247  chintcli  26249  fin2so  30040  intidl  30426  mzpincl  30666  elimaint  37764  elintima  37765

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-v 3111  df-int 4287