  Recently we proved (EPRSY, ERSTVY, ESY4, ESYY, EYY, EYY2, EYYrigi) that the
eigenvalue correlation functions of a general class of random matrices
converge, weakly with respect to the energy, to the corresponding ones of
Gaussian matrices. Tao and Vu \cite{TV5} gave a proof that for the special case
of Hermitian Wigner matrices the convergence can be strengthened to vague
convergence at any fixed energy in the bulk. In this article we show that this
theorem is an immediate corollary of our earlier results. Indeed, a more
general form of this theorem also follows directly from our work \cite{EKYY2}.
