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Theorem elrabf 2696
 Description: Membership in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.)
Hypotheses
Ref Expression
elrabf.1
elrabf.2
elrabf.3
elrabf.4
Assertion
Ref Expression
elrabf

Proof of Theorem elrabf
StepHypRef Expression
1 elex 2566 . 2
2 elex 2566 . . 3
4 df-rab 2315 . . . 4
54eleq2i 2104 . . 3
6 elrabf.1 . . . 4
7 elrabf.2 . . . . . 6
86, 7nfel 2186 . . . . 5
9 elrabf.3 . . . . 5
108, 9nfan 1457 . . . 4
11 eleq1 2100 . . . . 5
12 elrabf.4 . . . . 5
1311, 12anbi12d 442 . . . 4
146, 10, 13elabgf 2685 . . 3
155, 14syl5bb 181 . 2
161, 3, 15pm5.21nii 620 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349   wcel 1393  cab 2026  wnfc 2165  crab 2310  cvv 2557 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-rab 2315  df-v 2559 This theorem is referenced by:  elrab  2698  frind  4089  rabxfrd  4201
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