Consider the following premises. For all x_9, x_9 will cook if and only if x_9 will read a book. For all x_9, x_9 will cook if and only if x_9 will read a book. Can we infer the following from them? For all x_9, x_9 will cook if and only if x_9 will read a book.
That is one of the premises. Therefore, the answer is yes.