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Theorem elint 3621
 Description: Membership in class intersection. (Contributed by NM, 21-May-1994.)
Hypothesis
Ref Expression
elint.1
Assertion
Ref Expression
elint
Distinct variable groups:   ,   ,

Proof of Theorem elint
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elint.1 . 2
2 eleq1 2100 . . . 4
32imbi2d 219 . . 3
43albidv 1705 . 2
5 df-int 3616 . 2
61, 4, 5elab2 2690 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243   wcel 1393  cvv 2557  cint 3615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-int 3616 This theorem is referenced by:  elint2  3622  elintab  3626  intss1  3630  intss  3636  intun  3646  intpr  3647  peano1  4317
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