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

theorem
  for X be set, Y,Z be non empty set for f be Function of X,Y
  for g be Function of Y,Z holds f is onto & g is onto implies g*f is onto
proof
  let X be set, Y,Z be non empty set;
  let f be Function of X,Y;
  let g be Function of Y,Z;
  assume that
A1: f is onto and
A2: g is onto;
  rng f = Y by A1
    .= dom g by Def1;
  then rng(g*f) = rng g by RELAT_1:28
    .= Z by A2;
  hence thesis;
end;
