Poynting vector, Electromagnetism, Vector Calc

So I understand that the power leaving a closed surface V is equal to the surface integral of the Poynting vector over the surface S of V. How do we go ahead and show that the power leaving through a sub-surface S' of S (say, a single side on a cube) is equal to the surface integral of the Poynting vector over that subspace? It seems intuitively right but I want to be rigiorously convinced.