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

Theorem hbsbv 1814
Description: This is a version of hbsb 1820 with an extra distinct variable constraint, on and . (Contributed by Jim Kingdon, 25-Dec-2017.)
Hypothesis
Ref Expression
hbsbv.1
Assertion
Ref Expression
hbsbv
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem hbsbv
StepHypRef Expression
1 df-sb 1643 . 2
2 ax-17 1416 . . . 4
3 hbsbv.1 . . . 4
42, 3hbim 1434 . . 3
52, 3hban 1436 . . . 4
65hbex 1524 . . 3
74, 6hban 1436 . 2
81, 7hbxfrbi 1358 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbco2vlem  1817  2sb5rf  1862  2sb6rf  1863
  Copyright terms: Public domain W3C validator