Consider the following premises. For all x_10, if x_10 takes a plane, then x_10 is fast. For all x_10, if x_10 were fast, then x_10 is taking a plane. For all x_10, if x_10 were a soldier, then x_10 is taking a plane. For all x_10, if x_10 were fast, then x_10 is drinking water. For all x_10, x_10 will not drink water. For all x_10, if x_10 drinks water, then x_10 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is not a soldier.
 From the fact that for all x_10, if x_10 drinks water, then x_10 is fast, and that for all x_10, if x_10 were fast, then x_10 is drinking water we can infer that for all x_10, x_10 will drink water if and only if x_10 is fast via universal biconditional introduction. From the fact that for all x_10, x_10 will drink water if and only if x_10 is fast, and that for all x_10, x_10 will not drink water we can infer that for all x_10, x_10 is not fast via universal biconditional elimination. From the fact that for all x_10, if x_10 takes a plane, then x_10 is fast, and that for all x_10, if x_10 were fast, then x_10 is taking a plane we can infer that for all x_10, x_10 will take a plane if and only if x_10 is fast via universal biconditional introduction. From the fact that for all x_10, x_10 will take a plane if and only if x_10 is fast, and that for all x_10, x_10 is not fast we can infer that for all x_10, x_10 will not take a plane via universal biconditional elimination. Finally, from the fact that for all x_10, if x_10 were a soldier, then x_10 is taking a plane, and that for all x_10, x_10 will not take a plane we can infer that for all x_10, x_10 is not a soldier via universal modus tollens. Therefore, the answer is yes.