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Theorem elab2 2690
 Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.)
Hypotheses
Ref Expression
elab2.1
elab2.2
elab2.3
Assertion
Ref Expression
elab2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elab2
StepHypRef Expression
1 elab2.1 . 2
2 elab2.2 . . 3
3 elab2.3 . . 3
42, 3elab2g 2689 . 2
51, 4ax-mp 7 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:  elpw  3365  elint  3621  opabid  3994  elrn2  4576  elimasn  4692  oprabid  5537  tfrlem3a  5925  addnqprlemrl  6655  addnqprlemru  6656  addnqprlemfl  6657  addnqprlemfu  6658  mulnqprlemrl  6671  mulnqprlemru  6672  mulnqprlemfl  6673  mulnqprlemfu  6674  ltnqpr  6691  ltnqpri  6692  archpr  6741  cauappcvgprlemladdfu  6752  cauappcvgprlemladdfl  6753  caucvgprlemladdfu  6775  caucvgprprlemopu  6797
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