Yet Another Proof of Glivenko's Theorem

In this short note we give an alternative proof of Glivenko’s Theorem, stating that a formula $\varphi$ is provable in classical propositional logic if and only if $\mathrm{\neg }\mathrm{\neg }\varphi$ is provable in intuitionistic propositional logic. We work in the natural deduction system by Gentzen, and the key lemma shows that in any proof one needs only one application of reductio ad absurdum.