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

theorem Th4:
  for f being Function of X,Y st Y <> {} & x in X holds f.x in rng f
proof
  let f be Function of X,Y;
  assume Y <> {};
  then dom f = X by Def1;
  hence thesis by FUNCT_1:def 3;
end;
