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Theorem elintrabg 4055
 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 2495 . 2
2 eleq1 2495 . . . 4
32imbi2d 308 . . 3
43ralbidv 2717 . 2
5 vex 2951 . . 3
65elintrab 4054 . 2
71, 4, 6vtoclbg 3004 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2697  crab 2701  cint 4042 This theorem is referenced by:  tskmid  8707  eltskm  8710  nobndlem6  25644  elpcliN  30627 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-rab 2706  df-v 2950  df-int 4043
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