Consider the following premises. For all z_3, if z_3 drinks water, then z_3 is sleeping. For all z_3, z_3 will read a book if and only if z_3 is a cashier. For all z_3, if z_3 sleeps, then z_3 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, if z_3 drinks water, then z_3 is a cashier.
 From the fact that for all z_3, z_3 will read a book if and only if z_3 is a cashier we can infer that for all z_3, if z_3 reads a book, then z_3 is a cashier via universal biconditional elimination. From the fact that for all z_3, if z_3 drinks water, then z_3 is sleeping, and that for all z_3, if z_3 sleeps, then z_3 is reading a book we can infer that for all z_3, if z_3 drinks water, then z_3 is reading a book via universal transitivity. Finally, from the fact that for all z_3, if z_3 drinks water, then z_3 is reading a book, and that for all z_3, if z_3 reads a book, then z_3 is a cashier we can infer that for all z_3, if z_3 drinks water, then z_3 is a cashier via universal transitivity. Therefore, the answer is yes.