  In the present paper we prove a uniqueness theorem for the regular static,
traversable wormhole solutions to the Einstein-phantom scalar field theory with
two asymptotically flat regions (ends). We show that when a certain condition
on the asymptotic values of the scalar field is imposed such solutions are
uniquely specified by their mass $M$ and the scalar charge $D$.The main
arguments in the proof are based on the positive energy theorem.
