Consider the following premises. For all x_7, x_7 is a nurse and x_7 is excited. For all x_7, if x_7 were happy, then x_7 is not a nurse. There is at least one x_7 for which x_7 is happy if and only if x_7 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a soldier.
 From the fact that for all x_7, x_7 is a nurse and x_7 is excited we can infer that for all x_7, x_7 is a nurse via universal simplification. From the fact that for all x_7, if x_7 were happy, then x_7 is not a nurse, and that for all x_7, x_7 is a nurse we can infer that for all x_7, x_7 is not happy via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 is happy if and only if x_7 is a soldier, and that for all x_7, x_7 is not happy we can infer that there is at least one x_7 for which x_7 is not a soldier via existential biconditional elimination, which contradicts that For all x_7, x_7 is a soldier. Therefore, the answer is no.