reserve R for Ring,
  V for RightMod of R,
  W,W1,W2,W3 for Submodule of V,
  u,u1, u2,v,v1,v2 for Vector of V,
  x,y,y1,y2 for object;

theorem
  W1 is Submodule of W2 & W1 is Submodule of W3 implies W1 is Submodule
  of W2 /\ W3
proof
  assume
A1: W1 is Submodule of W2 & W1 is Submodule of W3;
  now
    let v;
    assume v in W1;
    then v in W2 & v in W3 by A1,RMOD_2:8;
    hence v in W2 /\ W3 by Th3;
  end;
  hence thesis by RMOD_2:28;
end;
