reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;
reserve D for non empty set;
reserve p,q,r for PartialPredicate of D;

theorem Th43:
  for D being set holds PP_not(PP_False(D)) = PP_True(D)
  proof
    let D be set;
    set T = PP_True(D);
    set B = PP_False(D);
    set n = PP_not(B);
A1: dom B = D;
    hence dom n = dom T by Def2;
    let x;
    assume
A2: x in dom n;
    then B.x = FALSE by FUNCOP_1:7;
    hence n.x = TRUE by A1,A2,Def2
    .= T.x by A2,FUNCOP_1:7;
  end;
