Inductive definitions are ubiquitous in mathematics and computer science, and play an important role in knowledge representation. To date, several proof systems have been developed for inductive definitions. However, these systems are typically limited to stratified definitions, while many important definitions are not stratified. Inspired by logic programming, the logic FO(ID) has been developed as an extension of classical first-order logic with general inductive definitions that go beyond stratification. This paper presents a classical sequent calculus LFO(ID) for FO(ID), based on the sequent calculus LKID by Brotherston and Simpson, which formalizes the principle of mathematical induction. While syntactically remaining close to LKID, LFO(ID) covers a substantially larger class of inductive definitions. The soundness of LFO(ID) is proven, thereby showing that a relatively conservative adaptation of LKID is capable of handling the liberal forms of definitions in FO(ID), governed by the intricate well-founded semantics.