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Theorem elintrabg 3939
 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 2413 . 2
2 eleq1 2413 . . . 4
32imbi2d 307 . . 3
43ralbidv 2634 . 2
5 vex 2862 . . 3
65elintrab 3938 . 2
71, 4, 6vtoclbg 2915 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642   wcel 1710  wral 2614  crab 2618  cint 3926 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rab 2623  df-v 2861  df-int 3927 This theorem is referenced by: (None)
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