Consider the following premises. James is not writing a letter. If Mary sleeps, then James is writing a letter. If James writes a letter, then Mary is sleeping. Sarah is reading a book if and only if Mary is sleeping. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not reading a book.
 From the fact that if Mary sleeps, then James is writing a letter, and that if James writes a letter, then Mary is sleeping we can infer that Mary is sleeping if and only if James is writing a letter via biconditional introduction. From the fact that Mary is sleeping if and only if James is writing a letter, and that James is not writing a letter we can infer that Mary is not sleeping via biconditional elimination. Finally, from the fact that Sarah is reading a book if and only if Mary is sleeping, and that Mary is not sleeping we can infer that Sarah is not reading a book via biconditional elimination. Therefore, the answer is yes.