 If \(\Gamma \vdash_D \theta\), then we say that the sentence \(\theta\) is a deductive consequence of the set of sentences \(\Gamma\), and that the argument \(\langle \Gamma,\theta \rangle\) is deductively valid. A sentence \(\theta\) is a logical theorem, or a deductive logical truth, if \(\vdash_D \theta\). That is, \(\theta\) is a logical theorem if it is a deductive consequence of the empty set. A set \(\Gamma\) of sentences is consistent if there is no sentence \(\theta\) such that \(\Gamma \vdash_D \theta\) and \(\Gamma \vdash_D \neg \theta\). That is, a set is consistent if it does not entail a pair of contradictory opposite sentencess.