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Theorem elintrabg 4239
 Description: Membership in the intersection of a class abstraction. (Contributed by NM, 17-Feb-2007.)
Assertion
Ref Expression
elintrabg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem elintrabg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2474 . 2
2 eleq1 2474 . . . 4
32imbi2d 314 . . 3
43ralbidv 2842 . 2
5 vex 3061 . . 3
65elintrab 4238 . 2
71, 4, 6vtoclbg 3117 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1405   wcel 1842  wral 2753  crab 2757  cint 4226 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rab 2762  df-v 3060  df-int 4227 This theorem is referenced by:  tskmid  9247  eltskm  9250  ldsysgenld  28594  ldgenpisyslem1  28597  nobndlem6  30144  elpcliN  32890
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