Consider the following premises. For all x, if x were fast, then x is a soldier. For all x, if x were a soldier, then x is fast. Richard is not fast. Can we infer the following from them? If we can, name the inference rule being used: Richard is a soldier.
 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 we can infer that Richard is a soldier if and only if Richard is fast via universal instantiation. Finally, from the fact that Richard is a soldier if and only if Richard is fast, and that Richard is not fast we can infer that Richard is not a soldier via biconditional elimination, which contradicts that Richard is a soldier. Therefore, the answer is no.