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Theorem clelsb3 2544
 Description: Substitution applied to an atomic wff (class version of elsb3 2185). (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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1630 . . 3
21sbco2 2167 . 2
3 nfv 1630 . . . 4
4 eleq1 2502 . . . 4
53, 4sbie 2154 . . 3
65sbbii 1667 . 2
7 nfv 1630 . . 3
8 eleq1 2502 . . 3
97, 8sbie 2154 . 2
102, 6, 93bitr3i 268 1
 Colors of variables: wff set class Syntax hints:   wb 178  wsb 1659   wcel 1727 This theorem is referenced by:  hblem  2546  cbvreu  2936  sbcel1v  3230  sbcel1gvOLD  3231  rmo3  3264  kmlem15  8075  iuninc  24042  measiuns  24602  ballotlemodife  24786 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2435  df-clel 2438
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