 In IF first-order logic, syntactic scopes no longer determine the semantic relation of dependence. In the sentence \((\forall x)(\forall y)(\exists z/\forall y) R(x, y, z)\), for instance, \(\exists z\) is syntactically subordinate to both \(\forall x\) and \(\forall y\), but is marked as independent of \(\forall y\), and is hence dependent only on \(\forall x\). Semantically this means that the witness of \(\exists z\) must be given by a function taking as an argument the interpretation of \(\forall x\), but not that of \(\forall y\). In order for \((\forall x)(\forall y)(\exists z/\forall y) R(x, y, z)\) to be true in \(M\), there must be a function \(f\) of one argument such that \(R(a, b, f(a))\) holds in \(M\), for any \(a\) interpreting \(\forall x\) and any \(b\) interpreting \(\forall y\).