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Theorem clelsb3 2351
 Description: Substitution applied to an atomic wff (class version of elsb3 2063). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
clelsb3
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem clelsb3
StepHypRef Expression
1 nfv 1629 . . 3
21sbco2 1980 . 2
3 nfv 1629 . . . 4
4 eleq1 2313 . . . 4
53, 4sbie 1910 . . 3
65sbbii 1885 . 2
7 nfv 1629 . . 3
8 eleq1 2313 . . 3
97, 8sbie 1910 . 2
102, 6, 93bitr3i 268 1
 Colors of variables: wff set class Syntax hints:   wb 178   wcel 1621  wsb 1882 This theorem is referenced by:  hblem  2353  cbvreu  2707  sbcel1gv  2980  rmo3  3006  kmlem15  7674 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-cleq 2246  df-clel 2249
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