reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem Th5:
  for f being Function of X,Y st Y <> {} & x in X holds f.x in Y
proof
  let f be Function of X,Y;
  assume Y <> {} & x in X;
  then f.x in rng f by Th4;
  hence thesis;
end;
