Consider the following premises. For all x, if x plays tennis, then x is fast. For all x, x is not a soldier. For all x, if x were a soldier, then x is fast. For all x, if x were fast, then x is a soldier. For all x, if x were fast, then x is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not play tennis.
 From the fact that for all x, if x were fast, then x is playing tennis, and that for all x, if x plays tennis, then x is fast we can infer that for all x, x is fast if and only if x will play tennis via universal biconditional introduction. From the fact that for all x, if x were a soldier, then x is fast, and that for all x, if x were fast, then x is a soldier we can infer that for all x, x is a soldier if and only if x is fast via universal biconditional introduction. From the fact that for all x, x is a soldier if and only if x is fast, and that for all x, x is not a soldier we can infer that for all x, x is not fast via universal biconditional elimination. Finally, from the fact that for all x, x is fast if and only if x will play tennis, and that for all x, x is not fast we can infer that for all x, x will not play tennis via universal biconditional elimination. Therefore, the answer is yes.