 where the variables \(x_{1}\), …, \(x_{n}\), \(y\) are all distinct, and the definiens in each case satisfies conditions that can be separated into a general and a specific  part.[7]  The general condition on definiens is the same in each case: it must not contain the defined term or any free variables other than those in the definiendum. The general conditions remain the same when the traditional account of definition is applied to non-classical logics (e.g., to many-valued and modal logics). The specific conditions are more variable. In classical logic, the specific condition on the definiens \(\psi(x)\) of (7) is that it satisfy an existence and uniqueness condition: that it be provable that something satisfies \(\psi(x)\) and that at most one thing satisfies  \(\psi(x)\).[8]  There are no specific conditions on (8), but the condition on (9) parallels that on (7). An existence and uniqueness claim must hold: the universal closure of the formula