Consider the following premises. For all x_8, x_8 is not rich. For all x_8, if x_8 drives a car, then x_8 is rich. For all x_8, if x_8 were rich, then x_8 is reading a book. For all x_8, x_8 will read a book if and only if x_8 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not read a book.
 From the fact that for all x_8, x_8 will read a book if and only if x_8 will drive a car we can infer that for all x_8, if x_8 reads a book, then x_8 is driving a car via universal biconditional elimination. From the fact that for all x_8, if x_8 reads a book, then x_8 is driving a car, and that for all x_8, if x_8 drives a car, then x_8 is rich we can infer that for all x_8, if x_8 reads a book, then x_8 is rich via universal transitivity. From the fact that for all x_8, if x_8 reads a book, then x_8 is rich, and that for all x_8, if x_8 were rich, then x_8 is reading a book we can infer that for all x_8, x_8 will read a book if and only if x_8 is rich via universal biconditional introduction. Finally, from the fact that for all x_8, x_8 will read a book if and only if x_8 is rich, and that for all x_8, x_8 is not rich we can infer that for all x_8, x_8 will not read a book via universal biconditional elimination. Therefore, the answer is yes.