Consider the following premises. It is not sunny. It is sunny if and only if John is reading a book. For all x_7, x_7 will cook if and only if x_7 will read a book. Can we infer the following from them? If we can, name the inference rule being used: John is not cooking.
 From the fact that for all x_7, x_7 will cook if and only if x_7 will read a book we can infer that John is cooking if and only if John is reading a book via universal instantiation. From the fact that it is sunny if and only if John is reading a book, and that it is not sunny we can infer that John is not reading a book via biconditional elimination. Finally, from the fact that John is cooking if and only if John is reading a book, and that John is not reading a book we can infer that John is not cooking via biconditional elimination. Therefore, the answer is yes.