The Interface Segregation Principle (ISP) and the Dependency Inversion Principle (DIP) are often presented as independent in textbooks and [1], but applying DIP’s ownership clause once per client–provider edge yields the same interfaces that ISP prescribes when DIP is interpreted causally coherently. This paper considers only class-level structural relationships. Under this hypothesis, applying DIP’s ownership clause per client always produces ISP-compliant segregation: DIP applied per client implies ISP universally. The converse—ISP implies DIP applied per client—is conditional and holds only under client-driven interface evolution. When interfaces are provider-driven (third-party APIs) or governed by shared negotiation (B2B contracts), ISP can be satisfied without satisfying DIP’s ownership clause. Therefore, the relationship is asymmetric: DIP applied per client implies ISP universally at the class level, but ISP implies DIP applied per client only under client-driven evolution. Under causal interpretation of DIP’s ownership clause, ISP makes explicit the granularity constraint that is already logically implicit in DIP: an interface owned by a client cannot contain functionality beyond what that client requires, otherwise changes would lack causal grounding in client requirements.The proof requires no formal machinery beyond the definitions of DIP and ISP restated in this paper.Several prior authors have argued that SOLID’s five heuristics are not all independent, but, to the author’s knowledge, the specific derivation—that DIP’s ownership clause applied per client is ISP—has not previously been identified in the literature. This paper examines why the connection went unnoticed for nearly thirty years; the most fundamental factor is that both heuristics were stated informally, making logical derivation impossible until they are stated precisely.