reserve V for RealLinearSpace;
reserve W,W1,W2,W3 for Subspace of V;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a,a1,a2 for Real;
reserve X,Y,x,y,y1,y2 for set;

theorem Th3:
 for x being object holds x in W1 /\ W2 iff x in W1 & x in W2
proof let x be object;
  x in W1 /\ W2 iff x in the carrier of W1 /\ W2 by STRUCT_0:def 5;
  then 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 by STRUCT_0:def 5;
end;
