Consider the following premises. For all x_7, x_7 will read a book if and only if x_7 is excited. For all x_7, x_7 will drink water if and only if x_7 is excited. For all x_7, x_7 is not a cashier. For all x_7, x_7 is a cashier if and only if x_7 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will drink water.
 From the fact that for all x_7, x_7 is a cashier if and only if x_7 will read a book, and that for all x_7, x_7 is not a cashier we can infer that for all x_7, x_7 will not read a book via universal biconditional elimination. From the fact that for all x_7, x_7 will read a book if and only if x_7 is excited, and that for all x_7, x_7 will not read a book we can infer that for all x_7, x_7 is not excited via universal biconditional elimination. Finally, from the fact that for all x_7, x_7 will drink water if and only if x_7 is excited, and that for all x_7, x_7 is not excited we can infer that for all x_7, x_7 will not drink water via universal biconditional elimination, which contradicts that There is at least one x_7 for which x_7 will drink water. Therefore, the answer is no.