Consider the following premises. For all x_15, if x_15 plays squash, then x_15 is playing tennis. For all x_15, if x_15 were rich, then x_15 is reading a book. For all x_15, x_15 will play squash if and only if x_15 will read a book. For all x_15, x_15 is a nurse if and only if x_15 will read a book. For all x_15, x_15 is rich or x_15 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will play tennis.
 From the fact that for all x_15, x_15 is a nurse if and only if x_15 will read a book we can infer that for all x_15, if x_15 were a nurse, then x_15 is reading a book via universal biconditional elimination. From the fact that for all x_15, if x_15 were rich, then x_15 is reading a book, that for all x_15, if x_15 were a nurse, then x_15 is reading a book, and that for all x_15, x_15 is rich or x_15 is a nurse we can infer that for all x_15, x_15 will read a book via universal disjunction elimination. From the fact that for all x_15, x_15 will play squash if and only if x_15 will read a book we can infer that for all x_15, if x_15 reads a book, then x_15 is playing squash via universal biconditional elimination. From the fact that for all x_15, if x_15 reads a book, then x_15 is playing squash, and that for all x_15, if x_15 plays squash, then x_15 is playing tennis we can infer that for all x_15, if x_15 reads a book, then x_15 is playing tennis via universal transitivity. Finally, from the fact that for all x_15, if x_15 reads a book, then x_15 is playing tennis, and that for all x_15, x_15 will read a book we can infer that for all x_15, x_15 will play tennis via universal modus ponens. Therefore, the answer is yes.