reserve X for set;
reserve UN for Universe;

theorem
  for u,v being Element of UN holds
  the set of all f where f is Function of u,v is Element of UN
  proof
    let u,v be Element of UN;
    set S = the set of all f where f is Function of u,v;
    S is Subset of bool [: u, v :]
    proof
      now
        let o be object;
        assume o in S;
        then ex f be Function of u,v st o = f;
        hence o in bool [:u,v:];
      end;
      then S c= bool [:u,v:];
      hence thesis;
    end;
    hence thesis by Th13;
  end;
