  In the setup of abstract elementary classes satisfying a local version of
superstability, we prove the uniqueness property for $\mu$-forking, a certain
independence notion arising from splitting. This had been a longstanding
technical difficulty when constructing forking-like notions in this setup. As
an application, we show that the two versions of forking symmetry appearing in
the literature (the one defined by Shelah for good frames and the one defined
by VanDieren for splitting) are equivalent.
