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Theorem clelab 2601
Description: Membership of a class variable in a class abstraction. (Contributed by NM, 23-Dec-1993.) (Proof shortened by Wolf Lammen, 16-Nov-2019.)
Assertion
Ref Expression
clelab
Distinct variable group:   ,

Proof of Theorem clelab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clel 2452 . 2
2 nfv 1707 . . 3
3 nfv 1707 . . . 4
4 nfsab1 2446 . . . 4
53, 4nfan 1928 . . 3
6 eqeq1 2461 . . . 4
7 sbequ12 1992 . . . . 5
8 df-clab 2443 . . . . 5
97, 8syl6bbr 263 . . . 4
106, 9anbi12d 710 . . 3
112, 5, 10cbvex 2022 . 2
121, 11bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  {cab 2442
This theorem is referenced by:  elrabi  3254  bj-csbsnlem  34470  frege55c  37945
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-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452
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