 The introduction clause for the universal quantifier is a bit more complicated. Suppose that a sentence \(\theta\) contains a closed term \(t\), and that \(\theta\) has been deduced from a set of premises \(\Gamma\). If the closed term \(t\) does not occur in any member of \(\Gamma\), then \(\theta\) will hold no matter which object \(t\) may denote. That is, \(\forall v \theta\) follows. 