Consider the following premises. There is at least one y_2 for which y_2 will play tennis if and only if y_2 will drink water. For all y_2, y_2 will work if and only if y_2 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_2 for which if y_2 plays tennis, then y_2 is working.
 From the fact that for all y_2, y_2 will work if and only if y_2 will drink water we can infer that for all y_2, if y_2 drinks water, then y_2 is working via universal biconditional elimination. From the fact that there is at least one y_2 for which y_2 will play tennis if and only if y_2 will drink water we can infer that there is at least one y_2 for which if y_2 plays tennis, then y_2 is drinking water via existential biconditional elimination. Finally, from the fact that there is at least one y_2 for which if y_2 plays tennis, then y_2 is drinking water, and that for all y_2, if y_2 drinks water, then y_2 is working we can infer that there is at least one y_2 for which if y_2 plays tennis, then y_2 is working via existential transitivity. Therefore, the answer is yes.