Consider the following premises. For all x_4, if x_4 reads a book, then x_4 is a musician. There is at least one x_4 for which if x_4 were a musician, then x_4 is reading a book. For all x_4, x_4 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is a musician.
 From the fact that there is at least one x_4 for which if x_4 were a musician, then x_4 is reading a book, and that for all x_4, if x_4 reads a book, then x_4 is a musician we can infer that there is at least one x_4 for which x_4 is a musician if and only if x_4 will read a book via existential biconditional introduction. From the fact that there is at least one x_4 for which x_4 is a musician if and only if x_4 will read a book we can infer that there is at least one x_4 for which if x_4 were a musician, then x_4 is reading a book via existential biconditional elimination. Finally, from the fact that there is at least one x_4 for which if x_4 were a musician, then x_4 is reading a book, and that for all x_4, x_4 will not read a book we can infer that there is at least one x_4 for which x_4 is not a musician via existential modus tollens, which contradicts that For all x_4, x_4 is a musician. Therefore, the answer is no.