 Two sentences (in the language of theory \(\mathcal{T}\)) will be called intersubstitutable according to \(\mathcal{T}\) provided the truth of any claim of the form \(\Gamma \vdash_{\mathcal{T}} \alpha\) is unaffected by substitutions of one for the other within \(\alpha\) or within any of the sentences in \(\Gamma\). Finally, we assume that the language contains a connective \({\rightarrow}\) that serves, in some suitable sense, as a conditional. For purposes of the following definition, we don’t place any specific requirements on the behavior of this conditional. We can now define the notion of a Curry sentence for a sentence-theory pair.