Consider the following premises. There is at least one x_14 for which if x_14 drinks water, then x_14 is writing a letter. For all x_14, x_14 will write a letter if and only if x_14 will drink water. For all x_14, x_14 will write a letter if and only if x_14 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which if x_14 drinks water, then x_14 is a cashier.
 From the fact that for all x_14, x_14 will write a letter if and only if x_14 will drink water we can infer that for all x_14, if x_14 writes a letter, then x_14 is drinking water via universal biconditional elimination. From the fact that for all x_14, if x_14 writes a letter, then x_14 is drinking water, and that there is at least one x_14 for which if x_14 drinks water, then x_14 is writing a letter we can infer that there is at least one x_14 for which x_14 will write a letter if and only if x_14 will drink water via existential biconditional introduction. From the fact that for all x_14, x_14 will write a letter if and only if x_14 is a cashier we can infer that for all x_14, if x_14 writes a letter, then x_14 is a cashier via universal biconditional elimination. From the fact that there is at least one x_14 for which x_14 will write a letter if and only if x_14 will drink water we can infer that there is at least one x_14 for which if x_14 drinks water, then x_14 is writing a letter via existential biconditional elimination. Finally, from the fact that there is at least one x_14 for which if x_14 drinks water, then x_14 is writing a letter, and that for all x_14, if x_14 writes a letter, then x_14 is a cashier we can infer that there is at least one x_14 for which if x_14 drinks water, then x_14 is a cashier via existential transitivity. Therefore, the answer is yes.