 This process of manufacturing new identities from old is called deduction. Any identity that can be generated by deduction starting from a given set \(A\) of identities is called a consequence of \(A\). The set of all consequences of \(A\) is called the deductive closure of \(A\). We refer to \(A\) as an axiomatization of its deductive closure. A set that is its own deductive closure is said to be deductively closed. It is straightforward to show that a set is deductively closed if and only if it is the deductive closure of some set.