I introduce a novel hybrid calculus \(\mathbb {H}\) for the validities and invalidities of classical propositional logic. The calculus \(\mathbb {H}\) is different in nature from other hybrid calculi that can be found in the literature in that it does not include specific anti-sequent rules. Instead, I add to the sequent rules of classical propositional logic only two structural rules that allow us to introduce and eliminate anti-sequents in our derivations. The resultant system is much simpler than the existing systems in the literature. For one thing, it does not suffer from a proliferation of rules. For another, it is structurally complete: its admissible rules are all derivable.
