Maxflow of graph equal to value of flow plus maxflow of residual graph

I'm reviewing max flow min cut for an upcoming exam and one of the proofs relies on the fact that for any flow $$f$$ on graph $$G$$ and residual graph $$G_f$$, $$\mathrm{maxflow}(G) = \mathrm{val}(f) + \mathrm{maxflow}(G_f).$$

This seems to be intuitively true, but I can't seem to prove it. Any help would be appreciated!