Consider the following premises. For all y_4, y_4 is a poet if and only if y_4 will play squash. For all y_4, y_4 will play squash if and only if y_4 is a poet. Can we infer the following from them? For all y_4, y_4 is a poet if and only if y_4 will play squash.
That is one of the premises. Therefore, the answer is yes.