Consider the following premises. There is at least one x_1 for which if x_1 were a soldier, then x_1 is playing squash. For all x_1, x_1 will play squash. For all x_1, if x_1 plays squash, then x_1 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 is a soldier.
 From the fact that there is at least one x_1 for which if x_1 were a soldier, then x_1 is playing squash, and that for all x_1, if x_1 plays squash, then x_1 is a soldier we can infer that there is at least one x_1 for which x_1 is a soldier if and only if x_1 will play squash via existential biconditional introduction. From the fact that there is at least one x_1 for which x_1 is a soldier if and only if x_1 will play squash we can infer that there is at least one x_1 for which if x_1 plays squash, then x_1 is a soldier via existential biconditional elimination. Finally, from the fact that there is at least one x_1 for which if x_1 plays squash, then x_1 is a soldier, and that for all x_1, x_1 will play squash we can infer that there is at least one x_1 for which x_1 is a soldier via existential modus ponens. Therefore, the answer is yes.