This paper presents a novel implication-based method for logic minimization in large-scale, multi-level networks. It significantly reduces network size through repeated addition and removal of redundant subnetworks, utilizing multi-signal implications and relationships among these implications. These are handled on a transitive implication graph, proposed in this paper, which offers the practical use of implications for logic minimization. The proposed method holds great promise for the achievement of an interactive logic design environment for large-scale networks.