reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;
reserve A,B for non empty set;
reserve Y for non empty set,
  f for Function of X,Y,
  p for PartFunc of Y,Z,
  x for Element of X;
reserve g for Function of X,X;
reserve X,Y for non empty set,
  Z,S,T for set,
  f for Function of X,Y,
  g for PartFunc of Y,Z,
  x for Element of X;

theorem
  for f being Function of P,Q holds { f } is FUNCTION_DOMAIN of P,Q
proof
  let f be Function of P,Q;
  for g be Element of { f } holds g is Function of P,Q by TARSKI:def 1;
  hence thesis by Def12;
end;
