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Theorem eliin 3662
 Description: Membership in indexed intersection. (Contributed by NM, 3-Sep-2003.)
Assertion
Ref Expression
eliin
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem eliin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2100 . . 3
21ralbidv 2326 . 2
3 df-iin 3660 . 2
42, 3elab2g 2689 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  wral 2306  ciin 3658 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-ral 2311  df-v 2559  df-iin 3660 This theorem is referenced by:  iinconstm  3666  iuniin  3667  iinss1  3669  ssiinf  3706  iinss  3708  iinss2  3709  iinab  3718  iundif2ss  3722  iindif2m  3724  iinin2m  3725  elriin  3727  iinpw  3742  xpiindim  4473  cnviinm  4859  iinerm  6178
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