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

Theorem cbvabw 2263
 Description: Version of cbvab 2264 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.)
Hypotheses
Ref Expression
cbvabw.1
cbvabw.2
cbvabw.3
Assertion
Ref Expression
cbvabw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvabw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvabw.1 . . . . 5
21sbco2v 1922 . . . 4
3 cbvabw.2 . . . . . 6
4 cbvabw.3 . . . . . 6
53, 4sbiev 1766 . . . . 5
65sbbii 1739 . . . 4
72, 6bitr3i 185 . . 3
8 df-clab 2127 . . 3
9 df-clab 2127 . . 3
107, 8, 93bitr4i 211 . 2
1110eqriv 2137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wnf 1437   wcel 1481  wsb 1736  cab 2126 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133 This theorem is referenced by:  cbvsbcw  2939
 Copyright terms: Public domain W3C validator