 We write an argument in the form \(\langle \Gamma, \phi \rangle\), where \(\Gamma\) is a set of sentences, the premises, and \(\phi\) is a single sentence, the conclusion. Remember that \(\Gamma\) may be empty. We write \(\Gamma \vdash \phi\) to indicate that \(\phi\) is deducible from \(\Gamma\), or, in other words, that the argument \(\langle \Gamma, \phi \rangle\) is deducible in \(D\). We may write \(\Gamma \vdash_D \phi\) to emphasize the deductive system \(D\). We write \(\vdash \phi\) or \(\vdash_D \phi\) to indicate that \(\phi\) can be deduced (in \(D)\) from the empty set of premises.