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Theorem elintrabg 3651
 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 2142 . 2
2 eleq1 2142 . . . 4
32imbi2d 228 . . 3
43ralbidv 2369 . 2
5 vex 2605 . . 3
65elintrab 3650 . 2
71, 4, 6vtoclbg 2660 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wral 2349  crab 2353  cint 3638 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rab 2358  df-v 2604  df-int 3639 This theorem is referenced by: (None)
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