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

theorem
  for f being Function of X,Y st Y <> {} & rng f = Y & f is one-to-one
  holds f"*f = id X & f*f" = id Y
proof
  let f be Function of X,Y;
  assume Y <> {};
  then dom f = X by Def1;
  hence thesis by FUNCT_1:39;
end;
