 Here is a typical application of the Unifying Principle. Suppose there is a procedure \(\cM\) which can be used to refute sets of sentences, and we wish to show it is complete for \(\cT\). For any set of sentences, let \(\Gamma(\cS)\) mean that \(\cS\) is not refutable by \(\cM\), and show that \(\Gamma\) is an abstract consistency property. Now suppose that \(\bA\) is a theorem of \(\cT\). Then \(\{\nsim \bA\}\) is inconsistent in \(\cT\), so by the Unifying Principle not \(\Gamma(\{\nsim \bA\})\), so \(\{\nsim \bA\}\) is refutable by \(\cM\).