Consider the following premises. For all y_4, y_4 will play tennis if and only if y_4 will drink water. For all y_4, y_4 will play tennis or y_4 will not drink water. Can we infer the following from them? There is at least one y_4 for which if is not true that y_4 will drink water if and only if y_4 will play tennis.
 From the fact that for all y_4, y_4 will play tennis or y_4 will not drink water we can infer that for all y_4, if y_4 drinks water, then y_4 is playing tennis. From the fact that for all y_4, y_4 will play tennis if and only if y_4 will drink water we can infer that for all y_4, if y_4 plays tennis, then y_4 is drinking water. Finally, from the fact that for all y_4, if y_4 drinks water, then y_4 is playing tennis, and that for all y_4, if y_4 plays tennis, then y_4 is drinking water we can infer that for all y_4, y_4 will drink water if and only if y_4 will play tennis, which contradicts that There is at least one y_4 for which if is not true that y_4 will drink water if and only if y_4 will play tennis. Therefore, the answer is no.