
theorem Th4:
  for X,Y being set, f being Function of X,Y holds
  f is onto iff [:f,f:] is onto
proof
  let X,Y be set, f be Function of X,Y;
  rng[:f,f:] = [:rng f, rng f:] by FUNCT_3:67;
  then rng f = Y iff rng[:f,f:] = [:Y,Y:] by ZFMISC_1:92;
  hence thesis;
end;
