Consider the following premises. For all x_10, if x_10 plays tennis, then x_10 is drinking water. For all x_10, if x_10 reads a book, then x_10 is playing tennis. For all x_10, x_10 will drink water if and only if x_10 will read a book. Can we infer the following from them? If we can, name the inference rule being used: If Patricia reads a book, then Patricia is playing tennis.
 From the fact that for all x_10, x_10 will drink water if and only if x_10 will read a book we can infer that for all x_10, if x_10 drinks water, then x_10 is reading a book via universal biconditional elimination. From the fact that for all x_10, if x_10 plays tennis, then x_10 is drinking water, and that for all x_10, if x_10 drinks water, then x_10 is reading a book we can infer that for all x_10, if x_10 plays tennis, then x_10 is reading a book via universal transitivity. From the fact that for all x_10, if x_10 plays tennis, then x_10 is reading a book, and that for all x_10, if x_10 reads a book, then x_10 is playing tennis we can infer that for all x_10, x_10 will play tennis if and only if x_10 will read a book via universal biconditional introduction. From the fact that for all x_10, x_10 will play tennis if and only if x_10 will read a book we can infer that Patricia is playing tennis if and only if Patricia is reading a book via universal instantiation. Finally, from the fact that Patricia is playing tennis if and only if Patricia is reading a book we can infer that if Patricia reads a book, then Patricia is playing tennis via biconditional elimination. Therefore, the answer is yes.