theorem
  for X being set, f being X-valued Function for x being set st x in dom
  f holds f.x in X
proof
  let X be set, f be X-valued Function;
  let x be set;
  assume x in dom f;
  then
A1: f.x in rng f by Def3;
  rng f c= X by RELAT_1:def 19;
  hence thesis by A1;
end;
