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Theorem elintg 4266
 Description: Membership in class intersection, with the sethood requirement expressed as an antecedent. (Contributed by NM, 20-Nov-2003.)
Assertion
Ref Expression
elintg
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elintg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2501 . 2
2 eleq1 2501 . . 3
32ralbidv 2871 . 2
4 vex 3090 . . 3
54elint2 4265 . 2
61, 3, 5vtoclbg 3146 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437   wcel 1870  wral 2782  cint 4258 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-v 3089  df-int 4259 This theorem is referenced by:  elinti  4267  elrint  4300  onmindif  5531  onmindif2  6653  mremre  15452  toponmre  20031  1stcfb  20382  uffixfr  20860  plycpn  23101  insiga  28789  dfon2lem8  30214  trintALTVD  36907  trintALT  36908  intsaluni  37725  intsal  37726
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