 Proof: Suppose that \(\Gamma\) is consistent and let \(\theta\) be any sentence. Then either it is not the case that \(\Gamma \vdash \theta\) or it is not the case that \(\Gamma \vdash \neg \theta\). For the converse, suppose that \(\Gamma\) is inconsistent and let \(\psi\) be any sentence. We have that there is a sentence such that both \(\Gamma \vdash \theta\) and \(\Gamma \vdash \neg \theta\). By ex falso quodlibet (Theorem 10), \(\Gamma \vdash \psi\). 