 Proof: Suppose that \(\Gamma_1 \vdash \theta\) and \(\Gamma_2 \vdash \neg \theta\). Then by Theorem \(8, \Gamma_1,\neg \psi \vdash \theta\), and \(\Gamma_2,\neg \psi \vdash \neg \theta\). So by \((\neg\)I), \(\Gamma_1, \Gamma_2 \vdash \neg \neg \psi\). By (DNE), \(\Gamma_1, \Gamma_2 \vdash \psi\). 