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Theorem clelab 2162
 Description: Membership of a class variable in a class abstraction. (Contributed by NM, 23-Dec-1993.)
Assertion
Ref Expression
clelab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem clelab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clab 2027 . . . 4
21anbi2i 430 . . 3
32exbii 1496 . 2
4 df-clel 2036 . 2
5 nfv 1421 . . 3
6 nfv 1421 . . . 4
7 nfs1v 1815 . . . 4
86, 7nfan 1457 . . 3
9 eqeq1 2046 . . . 4
10 sbequ12 1654 . . . 4
119, 10anbi12d 442 . . 3
125, 8, 11cbvex 1639 . 2
133, 4, 123bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wceq 1243  wex 1381   wcel 1393  wsb 1645  cab 2026 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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036 This theorem is referenced by:  elrabi  2695
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