Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  clelsb3 Structured version   Visualization version   Unicode version

Theorem clelsb3 2577
 Description: Substitution applied to an atomic wff (class version of elsb3 2283). (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 1769 . . 3
21sbco2 2264 . 2
3 nfv 1769 . . . 4
4 eleq1 2537 . . . 4
53, 4sbie 2257 . . 3
65sbbii 1812 . 2
7 nfv 1769 . . 3
8 eleq1 2537 . . 3
97, 8sbie 2257 . 2
102, 6, 93bitr3i 283 1
 Colors of variables: wff setvar class Syntax hints:   wb 189  wsb 1805   wcel 1904 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806  df-cleq 2464  df-clel 2467 This theorem is referenced by:  hblem  2579  cbvreu  3003  sbcel1v  3314  rmo3  3344  kmlem15  8612  iuninc  28253  measiuns  29113  ballotlemodife  29403  bj-nfcf  31595  sbcel1gvOLD  37318  ellimcabssub0  37794
 Copyright terms: Public domain W3C validator