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Theorem elab 2687
 Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 1-Aug-1994.)
Hypotheses
Ref Expression
elab.1
elab.2
Assertion
Ref Expression
elab
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elab
StepHypRef Expression
1 nfv 1421 . 2
2 elab.1 . 2
3 elab.2 . 2
41, 2, 3elabf 2686 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  cab 2026  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-v 2559 This theorem is referenced by:  ralab  2701  rexab  2703  intab  3644  dfiin2g  3690  dfiunv2  3693  uniuni  4183  peano5  4321  finds  4323  finds2  4324  funcnvuni  4968  fun11iun  5147  elabrex  5397  abrexco  5398  indpi  6440  nqprm  6640  nqprrnd  6641  nqprdisj  6642  nqprloc  6643  nqprl  6649  nqpru  6650  cauappcvgprlem2  6758  caucvgprlem2  6778  peano1nnnn  6928  peano2nnnn  6929  1nn  7925  peano2nn  7926  dfuzi  8348  shftfvalg  9419  ovshftex  9420  shftfval  9422  bj-ssom  10060
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