reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem Th9:
  X c= CnPos(X)
proof
  let a be object;
  assume
A1: a in X;
  then reconsider t = a as Element of HP-WFF;
  for T st T is Hilbert_theory & X c= T holds t in T by A1;
  hence thesis by Def11;
end;
