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;

theorem
  for A,B being non empty set, x being Element of A, f being Function of
  A,B holds f.x in rng f
proof
  let A,B be non empty set, x be Element of A, f be Function of A,B;
  dom f = A by Def1;
  hence thesis by FUNCT_1:def 3;
end;
