Consider the following premises. For all z_4, if z_4 were poor, then z_4 is excited. There is at least one z_4 for which z_4 is poor or z_4 is not excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_4 for which if z_4 were poor, then z_4 is excited.
 From the fact that there is at least one z_4 for which z_4 is poor or z_4 is not excited we can infer that there is at least one z_4 for which if z_4 were excited, then z_4 is poor via existential rewriting. From the fact that for all z_4, if z_4 were poor, then z_4 is excited, and that there is at least one z_4 for which if z_4 were excited, then z_4 is poor we can infer that there is at least one z_4 for which z_4 is poor if and only if z_4 is excited via existential biconditional introduction. Finally, from the fact that there is at least one z_4 for which z_4 is poor if and only if z_4 is excited we can infer that there is at least one z_4 for which if z_4 were poor, then z_4 is excited via existential biconditional elimination. Therefore, the answer is yes.