Consider the following premises. There is at least one x_7 for which if x_7 were a soldier, then x_7 is a lawyer. For all x_7, if x_7 were a lawyer, then x_7 is rich. For all x_7, x_7 is a soldier or x_7 is not excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which if x_7 were excited, then x_7 is rich.
 From the fact that for all x_7, x_7 is a soldier or x_7 is not excited we can infer that for all x_7, if x_7 were excited, then x_7 is a soldier via universal rewriting. From the fact that there is at least one x_7 for which if x_7 were a soldier, then x_7 is a lawyer, and that for all x_7, if x_7 were a lawyer, then x_7 is rich we can infer that there is at least one x_7 for which if x_7 were a soldier, then x_7 is rich via existential transitivity. Finally, from the fact that for all x_7, if x_7 were excited, then x_7 is a soldier, and that there is at least one x_7 for which if x_7 were a soldier, then x_7 is rich we can infer that there is at least one x_7 for which if x_7 were excited, then x_7 is rich via existential transitivity. Therefore, the answer is yes.