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Theorem elinti 4051
 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 4050 . . 3
2 eleq2 2496 . . . 4
32rspccv 3041 . . 3
41, 3syl6bi 220 . 2
54pm2.43i 45 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725  wral 2697  cint 4042 This theorem is referenced by:  inttsk  8641  subgint  14956  subrgint  15882  lssintcl  16032  ufinffr  17953  shintcli  22823  insiga  24512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-int 4043
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