I found this in the Texas Transportation Code
Sec. 547.602. MIRRORS REQUIRED. A motor vehicle, including a motor vehicle used to tow another vehicle, shall be equipped with a mirror
located to reflect to the operator a view of the highway for a distance of at least 200 feet from the rear of the vehicle.
Seems to indicate that your rear-view mirror alone is sufficient in satisfying the requirements. I have no side mirrors and have driven side-by-side with police cars down the road on multiple occasions with no problems. However, I HATE not having side mirrors and plan to address this soon.