The processa + E → a + E, whereEis an exotic baryon, is relevant to the inclusive reactiona + b → c + X, withErepresenting the (cb) system. The theorem proves that an amplitude which vanishes when (aE) is exotic and which also vanishes for exotic exchanges in the (aa) channel must vanishfor any octet meson a, even when (aE) is not exotic. Thus in a kinematic region where the inclusive reaction is described by coupling the conventional Regge trajectories to the (aa) channel and exotic exchanges are forbidden, an amplitude which vanishes when (abc) is exotic will also vanish when (bc) is exotic and (abc) is not exotic; i.e. whenever the fragmentation vertexb → cinvolves an exotic exchange.The assumption that certain “exotic” amplitudes vanish in inclusive reactions1has been shown to lead under certain reasonable assumptions to the conclusions that certain other amplitudes must also vanish, even though they are not normally considered exotic.2The exact implications and the validity of this result have been questioned. We present here a theorem which provides a concise and systematic statement of which nonexotic amplitudes must also vanish when the criterion of Chanet alis assumed.1We do not enter into the dynamical discussion of which criterion of exoticity is the proper one to use for inclusive reactions. This is a matter to be settled by experiment.