  Consider a strictly hyperbolic $n\times n$ system of conservation laws, where
each characteristic field is either genuinely nonlinear or linearly degenerate.
In this standard setting, it is well known that there exists a Lipschitz
semigroup of weak solutions, defined on a domain of functions with small total
variation. If the system admits a strictly convex entropy, we give a short
proof that every entropy weak solution taking values within the domain of the
semigroup coincides with a semigroup trajectory. The result shows that the
assumptions of ``Tame Variation" or ``Tame Oscillation", previously used to
achieve uniqueness, can be removed in the presence of a strictly convex
entropy.
