Consider the following premises. There is at least one x_8 for which if x_8 were a bartender, then x_8 is a poet. For all x_8, if x_8 were a poet, then x_8 is drinking water. For all x_8, x_8 is a bartender if and only if x_8 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is a poet if and only if x_8 is a bartender.
 From the fact that for all x_8, x_8 is a bartender if and only if x_8 will drink water we can infer that for all x_8, if x_8 drinks water, then x_8 is a bartender via universal biconditional elimination. From the fact that for all x_8, if x_8 were a poet, then x_8 is drinking water, and that for all x_8, if x_8 drinks water, then x_8 is a bartender we can infer that for all x_8, if x_8 were a poet, then x_8 is a bartender via universal transitivity. Finally, from the fact that for all x_8, if x_8 were a poet, then x_8 is a bartender, and that there is at least one x_8 for which if x_8 were a bartender, then x_8 is a poet we can infer that there is at least one x_8 for which x_8 is a poet if and only if x_8 is a bartender via existential biconditional introduction. Therefore, the answer is yes.