Theorem elinti 4295

Description: Membership in class intersection. (Contributed by NM, 14-Oct-1999.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
elinti

Proof of Theorem elinti

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		elintg 4294	. . 3
2		eleq2 2530	. . . 4
3	2	rspccv 3207	. . 3
4	1, 3	syl6bi 228	. 2
5	4	pm2.43i 47	1

Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  |^|cint 4286

This theorem is referenced by:  inttsk  9173  subgint  16225  subrgint  17451  lssintcl  17610  ufinffr  20430  shintcli  26247  insiga  28137

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