Consider the following premises. There is at least one y_1 for which y_1 will read a book if and only if y_1 will play tennis. For all y_1, y_1 will play tennis if and only if y_1 will read a book. Can we infer the following from them? There is at least one y_1 for which if y_1 reads a book, then y_1 is playing tennis.
 From the fact that there is at least one y_1 for which y_1 will read a book if and only if y_1 will play tennis we can infer that there is at least one y_1 for which if y_1 plays tennis, then y_1 is reading a book. From the fact that for all y_1, y_1 will play tennis if and only if y_1 will read a book we can infer that for all y_1, if y_1 reads a book, then y_1 is playing tennis. From the fact that there is at least one y_1 for which if y_1 plays tennis, then y_1 is reading a book, and that for all y_1, if y_1 reads a book, then y_1 is playing tennis we can infer that there is at least one y_1 for which y_1 will play tennis if and only if y_1 will read a book. Finally, from the fact that there is at least one y_1 for which y_1 will play tennis if and only if y_1 will read a book we can infer that there is at least one y_1 for which if y_1 reads a book, then y_1 is playing tennis. Therefore, the answer is yes.