  We consider $N\times N$ Hermitian Wigner random matrices $H$ where the
probability density for each matrix element is given by the density $\nu(x)=
e^{- U(x)}$. We prove that the eigenvalue statistics in the bulk is given by
Dyson sine kernel provided that $U \in C^6(\RR)$ with at most polynomially
growing derivatives and $\nu(x) \le C e^{- C |x|}$ for $x$ large. The proof is
based upon an approximate time reversal of the Dyson Brownian motion combined
with the convergence of the eigenvalue density to the Wigner semicircle law on
short scales.
