theorem
  for V being strict RightMod of R, W being strict Submodule of V holds
  (for v being Vector of V holds v in W) implies W = V
proof
  let V be strict RightMod of R, W be strict Submodule of V;
  assume for v being Vector of V holds v in W;
  then
A1: for v be Vector of V holds ( v in W iff v in V);
  V is Submodule of V by Th24;
  hence thesis by A1,Th30;
end;
