Consider the following premises. There is at least one x_1 for which if x_1 drinks water, then x_1 is a soldier. For all x_1, if x_1 were an artist, then x_1 is drinking water. For all x_1, x_1 is a soldier if and only if x_1 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 will drink water if and only if x_1 is a soldier.
 From the fact that for all x_1, x_1 is a soldier if and only if x_1 is an artist we can infer that for all x_1, if x_1 were a soldier, then x_1 is an artist via universal biconditional elimination. From the fact that for all x_1, if x_1 were a soldier, then x_1 is an artist, and that for all x_1, if x_1 were an artist, then x_1 is drinking water we can infer that for all x_1, if x_1 were a soldier, then x_1 is drinking water via universal transitivity. Finally, from the fact that there is at least one x_1 for which if x_1 drinks water, then x_1 is a soldier, and that for all x_1, if x_1 were a soldier, then x_1 is drinking water we can infer that there is at least one x_1 for which x_1 will drink water if and only if x_1 is a soldier via existential biconditional introduction. Therefore, the answer is yes.