theorem
  W1 is Subspace of W2 & W1 is Subspace of W3 implies W1 is Subspace of
  W2 /\ W3
proof
  assume
A1: W1 is Subspace of W2 & W1 is Subspace of W3;
  now
    let v;
    assume v in W1;
    then v in W2 & v in W3 by A1,VECTSP_4:8;
    hence v in W2 /\ W3 by Th3;
  end;
  hence thesis by VECTSP_4:28;
end;
