Consider the following premises. For all x_5, if x_5 were a musician, then x_5 is rich. For all x_5, if x_5 works, then x_5 is rich. For all x_5, x_5 is not a musician. For all x_5, if x_5 were rich, then x_5 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not work.
 From the fact that for all x_5, if x_5 were rich, then x_5 is a musician, and that for all x_5, if x_5 were a musician, then x_5 is rich we can infer that for all x_5, x_5 is rich if and only if x_5 is a musician via universal biconditional introduction. From the fact that for all x_5, x_5 is rich if and only if x_5 is a musician, and that for all x_5, x_5 is not a musician we can infer that for all x_5, x_5 is not rich via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 works, then x_5 is rich, and that for all x_5, x_5 is not rich we can infer that for all x_5, x_5 will not work via universal modus tollens. Therefore, the answer is yes.