  We prove universality of local eigenvalue statistics in the bulk of the
spectrum for orthogonal invariant matrix models with real analytic potentials
with one interval limiting spectrum. Our starting point is the Tracy-Widom
formula for the matrix reproducing kernel. The key idea of the proof is to
represent the differentiation operator matrix written in the basis of
orthogonal polynomials as a product of a positive Toeplitz matrix and a two
diagonal skew symmetric Toeplitz matrix.
