Consider the following premises. For all y_3, y_3 is a server if and only if y_3 will play squash. There is at least one y_3 for which y_3 will play squash if and only if y_3 is a server. Can we infer the following from them? For all y_3, if is not true that y_3 is a server if and only if y_3 will play squash.
That contradicts the premises. Therefore the answer is no.