A driver's license from one state is still valid if you drive through other states.
Explanation:
Article IV, Section 1 of the constitution states that "Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State and the Congress may by general Laws prescribe how such Acts, Records, and Proceedings shall be proved, and the Effect thereof".
This says that the courts of one state will accept or honor the judgment of other states without retrying the cause of action.
There will be a mutual understanding between each state. Hence if one drives from one state to another, a driver's license is valid.