Consider the following premises. If Patricia were an artist, then David is reading a book. Robert is not a doctor. If David reads a book, then Patricia is an artist. If Patricia were an artist, then Robert is a doctor. 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 if Patricia were an artist, then David is reading a book, and that if David reads a book, then Patricia is an artist we can infer that Patricia is an artist if and only if David is reading a book via biconditional introduction. From the fact that if Patricia were an artist, then Robert is a doctor, and that Robert is not a doctor we can infer that Patricia is not an artist via modus tollens. Finally, from the fact that Patricia is an artist if and only if David is reading a book, and that Patricia is not an artist we can infer that David is not reading a book via biconditional elimination. Therefore, the answer is yes.