reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem Th1:
  for f being Function holds f.x c= Union f
proof
  let f be Function;
  x in dom f or not x in dom f;
  then f.x in rng f or f.x = {} by FUNCT_1:3,def 2;
  hence thesis by ZFMISC_1:74;
end;
