14 U.S. Code § 711 - Exclusiveness of service
No member of the Reserve, other than a temporary member, may be a member of another military organization. A temporary member of the Reserve who is a member of another military component shall, if ordered to active duty therein, be disenrolled as a temporary member of the Reserve.
1981—Pub. L. 97–136 struck out provision that a member of the Reserve, other than a temporary member, is exempt from registration and liability for military training and service under any other law, and substituted “Exclusiveness of service” for “Exemption from military training and draft; exclusiveness of service” in section catchline.