Consider the following premises. There is at least one y_3 for which y_3 will play squash if and only if y_3 will read a book. For all y_3, y_3 will not play squash. For all y_3, y_3 will sleep if and only if y_3 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which y_3 will not sleep.
 From the fact that there is at least one y_3 for which y_3 will play squash if and only if y_3 will read a book, and that for all y_3, y_3 will not play squash we can infer that there is at least one y_3 for which y_3 will not read a book via existential biconditional elimination. From the fact that for all y_3, y_3 will sleep if and only if y_3 will read a book we can infer that for all y_3, if y_3 sleeps, then y_3 is reading a book via universal biconditional elimination. Finally, from the fact that for all y_3, if y_3 sleeps, then y_3 is reading a book, and that there is at least one y_3 for which y_3 will not read a book we can infer that there is at least one y_3 for which y_3 will not sleep via existential modus tollens. Therefore, the answer is yes.