Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  clelsb4 Unicode version

Theorem clelsb4 2143
 Description: Substitution applied to an atomic wff (class version of elsb4 1853). (Contributed by Jim Kingdon, 22-Nov-2018.)
Assertion
Ref Expression
clelsb4
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem clelsb4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1421 . . 3
21sbco2 1839 . 2
3 nfv 1421 . . . 4
4 eleq2 2101 . . . 4
53, 4sbie 1674 . . 3
65sbbii 1648 . 2
7 nfv 1421 . . 3
8 eleq2 2101 . . 3
97, 8sbie 1674 . 2
102, 6, 93bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wb 98   wcel 1393  wsb 1645 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036 This theorem is referenced by:  peano1  4317  peano2  4318
 Copyright terms: Public domain W3C validator