Consider the following premises. For all y_3, y_3 is a musician if and only if y_3 is poor. For all y_3, if y_3 were poor, then y_3 is sleeping. For all y_3, y_3 will sleep if and only if y_3 is poor. For all y_3, y_3 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: For all y_3, y_3 is not a musician.
 From the fact that for all y_3, y_3 will sleep if and only if y_3 is poor we can infer that for all y_3, if y_3 sleeps, then y_3 is poor via universal biconditional elimination. From the fact that for all y_3, if y_3 were poor, then y_3 is sleeping, and that for all y_3, if y_3 sleeps, then y_3 is poor we can infer that for all y_3, y_3 is poor if and only if y_3 will sleep via universal biconditional introduction. From the fact that for all y_3, y_3 is poor if and only if y_3 will sleep, and that for all y_3, y_3 will not sleep we can infer that for all y_3, y_3 is not poor via universal biconditional elimination. Finally, from the fact that for all y_3, y_3 is a musician if and only if y_3 is poor, and that for all y_3, y_3 is not poor we can infer that for all y_3, y_3 is not a musician via universal biconditional elimination. Therefore, the answer is yes.