 Theorem. Let \(\prec\) equal \(\prec_p\) and let \(\Bel_E = \Bel_{\prec_E}\). Then \(\Bel_{\mathcal{P}(W)}\) satisfies deductive cogency, Success, Cautious Monotony and Inclusion. Furthermore, \(\Bel_E = \alpha(\Pr)_E = \alpha(\Pr_E)\) for all \(E\in{\bf A}^{\Pr}\). 