MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  elabf Unicode version

Theorem elabf 3245
Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 1-Aug-1994.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
elabf.1
elabf.2
elabf.3
Assertion
Ref Expression
elabf
Distinct variable group:   ,

Proof of Theorem elabf
StepHypRef Expression
1 elabf.2 . 2
2 nfcv 2619 . . 3
3 elabf.1 . . 3
4 elabf.3 . . 3
52, 3, 4elabgf 3244 . 2
61, 5ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  e.wcel 1818  {cab 2442   cvv 3109
This theorem is referenced by:  elab  3246  dfon2lem1  29215  sdclem2  30235  sdclem1  30236
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
  Copyright terms: Public domain W3C validator