  The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe
phase separation in two-component systems interacting with an incompressible
fluid flow. We demonstrate the \emph{weak-strong uniqueness} result for this
system in a bounded domain in three spatial dimensions which implies that when
a strong solution exists then a weak solution emanating from the same data
coincides with the strong solution on its whole life-span. The proof of given
assertion relies on a form of a relative entropy method.
