  We present a new technique for proving empirical process invariance principle
for stationary processes $(X_n)_{n\geq 0}$. The main novelty of our approach
lies in the fact that we only require the central limit theorem and a moment
bound for a restricted class of functions $(f(X_n))_{n\geq 0}$, not containing
the indicator functions. Our approach can be applied to Markov chains and
dynamical systems, using spectral properties of the transfer operator. Our
proof consists of a novel application of chaining techniques.
