  A second form of v-Curry paradox arises for a theory \(\mathcal{T}_V\) whose subject-matter includes the single-premise consequence relation \(\vdash_{\mathcal{T}_{V}}\) that obtains, according to that very theory, between sentences in its  language.[30]  Let this relation be expressed by the predicate \(Val(x,y)\), and assume further that there is a sentence \(\chi\) that is either \(Val(\langle\chi\rangle, \langle\pi\rangle)\), or is at least intersubstitutable with the latter according to \(\mathcal{T}_V\). One form of v-Curry paradox employs two principles governing \(Val\), which we call “validity detachment” and “validity proof” following Beall &amp; Murzi (2013).