Consider the following premises. Michael is not taking a plane. For all z, z will read a book if and only if z is excited. David is excited if and only if Michael is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: David is not reading a book.
 From the fact that for all z, z will read a book if and only if z is excited we can infer that David is reading a book if and only if David is excited via universal instantiation. From the fact that David is excited if and only if Michael is taking a plane, and that Michael is not taking a plane we can infer that David is not excited via biconditional elimination. From the fact that David is reading a book if and only if David is excited we can infer that if David reads a book, then David is excited via biconditional elimination. Finally, from the fact that if David reads a book, then David is excited, and that David is not excited we can infer that David is not reading a book via modus tollens. Therefore, the answer is yes.