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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.
StepHypRef Expression
1 elintg 4294 . . 3
2 eleq2 2530 . . . 4
32rspccv 3207 . . 3
41, 3syl6bi 228 . 2
54pm2.43i 47 1
 Colors of variables: wff setvar class 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
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