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

Theorem sbnv 1765
Description: Version of sbn 1823 where and are distinct. (Contributed by Jim Kingdon, 18-Dec-2017.)
Assertion
Ref Expression
sbnv
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sbnv
StepHypRef Expression
1 sb6 1763 . . 3
2 alinexa 1491 . . 3
31, 2bitri 173 . 2
4 sb5 1764 . 2
53, 4xchbinxr 607 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98  wal 1240  wex 1378  wsb 1642
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-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-sb 1643
This theorem is referenced by:  sbn  1823
  Copyright terms: Public domain W3C validator