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Theorem elab2 2860
 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 2859 . 2
51, 4ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1335   wcel 2128  cab 2143  cvv 2712 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714 This theorem is referenced by:  elpw  3549  elint  3813  opabid  4217  elrn2  4827  elimasn  4952  oprabid  5850  tfrlem3a  6254  tfrcllemsucaccv  6298  tfrcllembxssdm  6300  tfrcllemres  6306  addnqprlemrl  7471  addnqprlemru  7472  addnqprlemfl  7473  addnqprlemfu  7474  mulnqprlemrl  7487  mulnqprlemru  7488  mulnqprlemfl  7489  mulnqprlemfu  7490  ltnqpr  7507  ltnqpri  7508  archpr  7557  cauappcvgprlemladdfu  7568  cauappcvgprlemladdfl  7569  caucvgprlemladdfu  7591  caucvgprprlemopu  7613  suplocexprlemloc  7635  txuni2  12627
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