Consider the following premises. For all x_9, x_9 will drink water or x_9 is a poet. For all x_9, if x_9 were a musician, then x_9 is a cashier. For all x_9, x_9 will not drink water. There is at least one x_9 for which x_9 is a cashier if and only if x_9 is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is a cashier.
 From the fact that for all x_9, x_9 will drink water or x_9 is a poet, and that for all x_9, x_9 will not drink water we can infer that for all x_9, x_9 is a poet via universal disjunctive syllogism. From the fact that there is at least one x_9 for which x_9 is a cashier if and only if x_9 is a poet we can infer that there is at least one x_9 for which if x_9 were a poet, then x_9 is a cashier via existential biconditional elimination. From the fact that for all x_9, x_9 is a poet we can infer that for all x_9, x_9 is a poet or x_9 is a musician via universal addition. Finally, from the fact that there is at least one x_9 for which if x_9 were a poet, then x_9 is a cashier, that for all x_9, if x_9 were a musician, then x_9 is a cashier, and that for all x_9, x_9 is a poet or x_9 is a musician we can infer that there is at least one x_9 for which x_9 is a cashier via existential disjunction elimination. Therefore, the answer is yes.