reconsider A = C, B = D as Subset of T ;
A5: A is open by Th1;
A6: B is open by Th1;
A7: A is closed by Th2;
A8: B is closed by Th2;
A /\ B is open by A5, A6;
hence C /\ D is Element of OpenClosedSet T by A7, A8, Th3; :: thesis: verum