Consider the following premises. For all x_5, if x_5 reads a book, then x_5 is playing tennis. There is at least one x_5 for which if x_5 plays tennis, then x_5 is drinking water. For all x_5, if x_5 plays tennis, then x_5 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which if x_5 reads a book, then x_5 is drinking water.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is playing tennis, and that for all x_5, if x_5 plays tennis, then x_5 is reading a book we can infer that for all x_5, x_5 will read a book if and only if x_5 will play tennis via universal biconditional introduction. From the fact that for all x_5, x_5 will read a book if and only if x_5 will play tennis we can infer that for all x_5, if x_5 reads a book, then x_5 is playing tennis via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 reads a book, then x_5 is playing tennis, and that there is at least one x_5 for which if x_5 plays tennis, then x_5 is drinking water we can infer that there is at least one x_5 for which if x_5 reads a book, then x_5 is drinking water via existential transitivity. Therefore, the answer is yes.