theorem
  for V being strict LeftMod of R, W being strict Submodule of V holds
  (for v being Vector of V holds v in W iff v in V) implies W = V
  proof
    let V be strict LeftMod of R, W be strict Submodule of V;
    assume
A1: for v being Vector of V holds v in W iff v in V;
    V is Submodule of V by Th32;
    hence thesis by A1,Th46;
  end;
