In the form outlined above, T-sentences express the equivalence between \(T\ulcorner \phi \urcorner\) and \(\phi\) only when \(\phi\) is a sentence. In order to capture the equivalence for properties \((x\) has property P iff ‘P’ is true of \(x)\) one must generalise the T-sentences. The result are usually referred to as the uniform T-senences and are formalised by the equivalences  \(\forall x(T\ulcorner \phi(\underline{x})\urcorner \leftrightarrow \phi(x))\) for each open formula \(\phi(v)\) with at most \(v\) free in \(\phi\). Underlining the variable indicates it is bound from the outside. More precisely, \(\ulcorner \phi(\underline{x})\urcorner\) stands for the result of replacing the variable \(v\) in \(\ulcorner \phi(v)\urcorner\) by the numeral of \(x\).