Consider the following premises. There is at least one x_1 for which if x_1 were a server, then x_1 is excited. For all x_1, if x_1 were poor, then x_1 is a server. For all x_1, if x_1 were excited, then x_1 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, if is not true that x_1 is poor if and only if x_1 is a server.
 From the fact that there is at least one x_1 for which if x_1 were a server, then x_1 is excited, and that for all x_1, if x_1 were excited, then x_1 is poor we can infer that there is at least one x_1 for which if x_1 were a server, then x_1 is poor via existential transitivity. Finally, from the fact that for all x_1, if x_1 were poor, then x_1 is a server, and that there is at least one x_1 for which if x_1 were a server, then x_1 is poor we can infer that there is at least one x_1 for which x_1 is poor if and only if x_1 is a server via existential biconditional introduction, which contradicts that For all x_1, if is not true that x_1 is poor if and only if x_1 is a server. Therefore, the answer is no.