Consider the following premises. For all x_9, if x_9 were poor, then x_9 is a musician. For all x_8, x_8 is a musician. For all x_9, if x_9 were a musician, then x_9 is poor. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not poor.
 From the fact that for all x_9, if x_9 were poor, then x_9 is a musician, and that for all x_9, if x_9 were a musician, then x_9 is poor we can infer that for all x_9, x_9 is poor if and only if x_9 is a musician via universal biconditional introduction. From the fact that for all x_8, x_8 is a musician we can infer that Joseph is a musician via universal instantiation. From the fact that for all x_9, x_9 is poor if and only if x_9 is a musician we can infer that Joseph is poor if and only if Joseph is a musician via universal instantiation. From the fact that Joseph is poor if and only if Joseph is a musician we can infer that if Joseph were a musician, then Joseph is poor via biconditional elimination. Finally, from the fact that if Joseph were a musician, then Joseph is poor, and that Joseph is a musician we can infer that Joseph is poor via modus ponens, which contradicts that Joseph is not poor. Therefore, the answer is no.