Abstractions of formal proofs, so-called abstract proof structures, serve as a well-accepted tool for studying structure and properties of formal proofs. Given a sequent calculus proof, there are various abstractions including proof skeleton, proof net and logical flow graph (in particular atomic flow graph). These abstract proof structures emerged in different areas of proof theory and a thorough investigation of their interrelationship does not exist so far. By introducing a tuple-based representation of proofs, which allows a suitable representation of the before-mentioned abstractions, we establish a uniform framework for classical first-order logic which clarifies the relationship between these proof structures in the context of the sequent calculus LK. We show that, in case of a suitable treatment of the weakening rules, there exists a structure for every pair of the above-mentioned abstractions such that both abstractions can be reduced to it. Besides the gained insights of the interrelationship by defining this uniform framework, we get a framework for generalizing results and algorithms. For instance, Krajicek and Pudlak introduced an algorithm defined on proof skeletons for deriving bounds on the minimal size of proofs. We generalize this result to proof nets by generalizing the algorithm to proof net skeletons. A proof net skeleton is an abstraction of both, proof nets and proof skeletons. Furthermore, we investigate the cardinalities of the equivalences generated by the abstractions. We show that there exist finitely many proofs having the same proof net (atomic flow graph). For proof skeletons there exists an infinite number of associated proofs.