  In this paper we show that a Brownian Gibbsian line ensemble is completely
characterized by the finite-dimensional marginals of its top curve, i.e. the
finite-dimensional sets of the its top curve form a separating class. A
particular consequence of our result is that the Airy line ensemble is the
unique Brownian Gibbsian line ensemble, whose top curve is the Airy$_2$
process.
