Symbolic model checkers can construct proofs of safety properties over complex models, but when a proof succeeds, the results do not generally provide much insight to the user. Recently, proof cores (alternately, for inductive model checkers, Inductive Validity Cores (IVCs)) were introduced to trace a property to a minimal set of model elements necessary for proof. Minimal IVCs facilitate several engineering tasks, including performing traceability and analyzing requirements completeness, that usually rely on the minimality of IVCs. However, existing algorithms for generating an IVC are either expensive or only able to find an approximately minimal IVC. Besides minimality, computing all minimal IVCs of a given property is an interesting problem that provides several useful analyses, including regression analysis for testing/proof, determination of the minimum (as opposed to minimal) number of model elements necessary for proof, the diversity examination of model elements leading to proof, and analyzing fault tolerance. This paper proposes an efficient method for finding all minimal IVCs of a given property proving its correctness and completeness. We benchmark our algorithm against existing IVC-generating algorithms and show, in many cases, the cost of finding all minimal IVCs by our technique is similar to finding a single minimal IVC using existing algorithms.