Consider the following premises. Joseph is not an electrician. If William reads a book, then Joseph is an electrician. Joseph is an electrician if and only if William is reading a book. Can we infer the following from them? If we can, name the inference rule being used: William is not reading a book.
 From the fact that Joseph is an electrician if and only if William is reading a book we can infer that if Joseph were an electrician, then William is reading a book via biconditional elimination. From the fact that if William reads a book, then Joseph is an electrician, and that if Joseph were an electrician, then William is reading a book we can infer that William is reading a book if and only if Joseph is an electrician via biconditional introduction. Finally, from the fact that William is reading a book if and only if Joseph is an electrician, and that Joseph is not an electrician we can infer that William is not reading a book via biconditional elimination. Therefore, the answer is yes.