We prove a single achievability theorem that recovers many achievability results in network information theory as simple corollaries. Our result is enabled by many novel elements such as a generalized network model that includes multiple sources and channels interacting with each other, a unified typicality constraint that generalizes cost and distortion constraints, a unified coding strategy that generalizes many coding schemes in the literature, and novel proof techniques. Our unified coding scheme performs at least as good as many previous schemes and sometimes better. Using our theorem, many new achievability results in network information theory can now be obtained without any tedious proof steps.