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 Th3:
  x in W1 /\ W2 iff x in W1 & x in W2
proof
  x in W1 /\ W2 iff x in (the carrier of W1) /\ (the carrier of W2) by
Def2;
  then x in W1 /\ W2 iff x in the carrier of W1 & x in the carrier of W2 by
XBOOLE_0:def 4;
  hence thesis;
end;
