Consider the following premises. For all x_5, if x_5 cooks, then x_5 is a janitor. For all x_5, if x_5 were a janitor, then x_5 is reading a book. For all x_5, if x_5 reads a book, then x_5 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, if x_5 cooks, then x_5 is reading a book.
 From the fact that for all x_5, if x_5 were a janitor, then x_5 is reading a book, and that for all x_5, if x_5 reads a book, then x_5 is a janitor we can infer that for all x_5, x_5 is a janitor if and only if x_5 will read a book via universal biconditional introduction. From the fact that for all x_5, x_5 is a janitor if and only if x_5 will read a book we can infer that for all x_5, if x_5 were a janitor, then x_5 is reading a book via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 cooks, then x_5 is a janitor, and that for all x_5, if x_5 were a janitor, then x_5 is reading a book we can infer that for all x_5, if x_5 cooks, then x_5 is reading a book via universal transitivity. Therefore, the answer is yes.