Consider the following premises. There is at least one x_3 for which x_3 will not read a book. For all x_3, if x_3 plays tennis, then x_3 is reading a book. For all x_3, x_3 will play tennis or x_3 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will play tennis.
 From the fact that for all x_3, x_3 will play tennis or x_3 will not read a book we can infer that for all x_3, if x_3 reads a book, then x_3 is playing tennis via universal rewriting. From the fact that for all x_3, if x_3 plays tennis, then x_3 is reading a book, and that for all x_3, if x_3 reads a book, then x_3 is playing tennis we can infer that for all x_3, x_3 will play tennis if and only if x_3 will read a book via universal biconditional introduction. Finally, from the fact that for all x_3, x_3 will play tennis if and only if x_3 will read a book, and that there is at least one x_3 for which x_3 will not read a book we can infer that there is at least one x_3 for which x_3 will not play tennis via existential biconditional elimination, which contradicts that For all x_3, x_3 will play tennis. Therefore, the answer is no.