New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  elrabf Unicode version

Theorem elrabf 2993
 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 2867 . 2
2 elex 2867 . . 3
4 df-rab 2623 . . . 4
54eleq2i 2417 . . 3
6 elrabf.1 . . . 4
7 elrabf.2 . . . . . 6
86, 7nfel 2497 . . . . 5
9 elrabf.3 . . . . 5
108, 9nfan 1824 . . . 4
11 eleq1 2413 . . . . 5
12 elrabf.4 . . . . 5
1311, 12anbi12d 691 . . . 4
146, 10, 13elabgf 2983 . . 3
155, 14syl5bb 248 . 2
161, 3, 15pm5.21nii 342 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wceq 1642   wcel 1710  cab 2339  wnfc 2476  crab 2618  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861 This theorem is referenced by:  elrab  2994
 Copyright terms: Public domain W3C validator