reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;

theorem
  for C being set, A being non empty set
  for f being Function of A,Funcs({} qua set,C),
      g being Function of A,{} holds rng (f..g) = {}
proof
  let C be set, A be non empty set;
  let f be Function of A, Funcs({} qua set,C), g be Function of A,{};
  set a = the Element of A;
  dom(f..g) = dom f /\ dom g by PRALG_1:def 19 .= {};
  hence thesis by RELAT_1:42;
end;
