Consider the following premises. For all x_15, x_15 will go running or x_15 will play squash. For all x_15, x_15 is sad if and only if x_15 will go running. For all x_15, x_15 is not poor. There is at least one x_15 for which x_15 is sad if and only if x_15 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 will play squash.
 From the fact that there is at least one x_15 for which x_15 is sad if and only if x_15 is poor, and that for all x_15, x_15 is not poor we can infer that there is at least one x_15 for which x_15 is not sad via existential biconditional elimination. From the fact that for all x_15, x_15 is sad if and only if x_15 will go running, and that there is at least one x_15 for which x_15 is not sad we can infer that there is at least one x_15 for which x_15 will not go running via existential biconditional elimination. Finally, from the fact that for all x_15, x_15 will go running or x_15 will play squash, and that there is at least one x_15 for which x_15 will not go running we can infer that there is at least one x_15 for which x_15 will play squash via existential disjunctive syllogism. Therefore, the answer is yes.