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

Theorem pwjust 3352
Description: Soundness justification theorem for df-pw 3353. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
pwjust  {  |  C_  }  {  | 
C_  }
Distinct variable groups:   ,   ,

Proof of Theorem pwjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseq1 2960 . . 3  C_  C_
21cbvabv 2158 . 2  {  |  C_  }  {  | 
C_  }
3 sseq1 2960 . . 3  C_  C_
43cbvabv 2158 . 2  {  |  C_  }  {  |  C_  }
52, 4eqtri 2057 1  {  |  C_  }  {  | 
C_  }
Colors of variables: wff set class
Syntax hints:   wceq 1242   {cab 2023    C_ wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator