Consider the following premises. For all x_6, if x_6 reads a book, then x_6 is working. For all x_6, x_6 will play tennis if and only if x_6 will work. There is at least one x_6 for which x_6 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not read a book.
 From the fact that for all x_6, x_6 will play tennis if and only if x_6 will work, and that there is at least one x_6 for which x_6 will not play tennis we can infer that there is at least one x_6 for which x_6 will not work via existential biconditional elimination. Finally, from the fact that for all x_6, if x_6 reads a book, then x_6 is working, and that there is at least one x_6 for which x_6 will not work we can infer that there is at least one x_6 for which x_6 will not read a book via existential modus tollens. Therefore, the answer is yes.