Consider the following premises. For all x_3, if x_3 were a server, then x_3 is a sailor. There is at least one x_3 for which if x_3 were a sailor, then x_3 is rich. For all x_3, if x_3 were rich, then x_3 is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which if x_3 were a server, then x_3 is a sailor.
 From the fact that there is at least one x_3 for which if x_3 were a sailor, then x_3 is rich, and that for all x_3, if x_3 were rich, then x_3 is a server we can infer that there is at least one x_3 for which if x_3 were a sailor, then x_3 is a server via existential transitivity. From the fact that there is at least one x_3 for which if x_3 were a sailor, then x_3 is a server, and that for all x_3, if x_3 were a server, then x_3 is a sailor we can infer that there is at least one x_3 for which x_3 is a sailor if and only if x_3 is a server via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 is a sailor if and only if x_3 is a server we can infer that there is at least one x_3 for which if x_3 were a server, then x_3 is a sailor via existential biconditional elimination. Therefore, the answer is yes.