 Suppose \(A_1, \ldots, A_n\) entail \(B\). Then \({\sim}B\) entails \({\sim}A_1\) or … or \({\sim}A_n\). Therefore \(\mathbf{p}({\sim}B) \le \mathbf{p}({\sim}A_1) + \cdots + \mathbf{p}({\sim}A_n)\): the improbability of the conclusion of a valid argument cannot exceed the sum of the improbabilities of the premises. 