reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;

theorem Th4:
  for x being Element of X holds x in f"{f.x}
proof
  let x be Element of X;
  f.x in {f.x} by TARSKI:def 1;
  hence thesis by FUNCT_2:38;
end;
