theorem Th14:
  X c= Y implies Cn(X) c= Cn(Y)
proof
  assume
A1: X c= Y;
  thus Cn(X) c= Cn(Y)
  proof
    let a be object;
    assume
A2: a in Cn(X);
    then reconsider t=a as Element of CQC-WFF(Al);
 for T st T is being_a_theory & Y c= T holds t in T
    proof
      let T such that
A3:   T is being_a_theory and
A4:   Y c= T;
   X c= T by A1,A4;
      hence thesis by A2,A3,Def2;
    end;
    hence thesis by Def2;
  end;
end;
