Consider the following premises. For all y_1, y_1 will play tennis. For all y_1, y_1 is bored or y_1 will not play tennis. There is at least one y_1 for which if y_1 drinks water, then y_1 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is bored.
 From the fact that for all y_1, y_1 is bored or y_1 will not play tennis we can infer that for all y_1, if y_1 plays tennis, then y_1 is bored via universal rewriting. From the fact that for all y_1, y_1 will play tennis we can infer that for all y_1, y_1 will play tennis or y_1 will drink water via universal addition. Finally, from the fact that for all y_1, if y_1 plays tennis, then y_1 is bored, that there is at least one y_1 for which if y_1 drinks water, then y_1 is bored, and that for all y_1, y_1 will play tennis or y_1 will drink water we can infer that there is at least one y_1 for which y_1 is bored via existential disjunction elimination. Therefore, the answer is yes.