A graph is called (matching-)immune if it has no edge cut that is also a matching. Farley and Proskurowski proved that for all immune graphs G=(V,E), |E|≥⌈3(|V|-1)/2⌉, and constructed a large class of immune graphs that attain this lower bound for every value of |V(G)|, called ABC graphs. They conjectured that every immune graph that attains this lower bound is an ABC graph. We present a proof of this conjecture.