It is shown that a theorem of Bilingsley ((1968) Convergence of Probability Measures, Wiley; Theorem 22.1) about weak convergence of empirical processes of $\varphi$-mixing sequences also holds for a class of strong-mixing sequences.
"A Note on Empirical Processes of Strong-Mixing Sequences." Ann. Probab. 1 (5) 870 - 875, October, 1973. https://doi.org/10.1214/aop/1176996855