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Theorem clelab 2558
 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 2425 . . . 4
21anbi2i 677 . . 3
32exbii 1593 . 2
4 df-clel 2434 . 2
5 nfv 1630 . . 3
6 nfv 1630 . . . 4
7 nfs1v 2184 . . . 4
86, 7nfan 1847 . . 3
9 eqeq1 2444 . . . 4
10 sbequ12 1945 . . . 4
119, 10anbi12d 693 . . 3
125, 8, 11cbvex 1984 . 2
133, 4, 123bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wceq 1653  wsb 1659   wcel 1726  cab 2424 This theorem is referenced by:  elrabi  3092 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434
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