Consider the following premises. For all x, x is a sailor if and only if x is a soldier. For all x, if x were a soldier, then x is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which the fact that x were a sailor does not imply that x is a soldier.
 From the fact that for all x, x is a sailor if and only if x is a soldier we can infer that for all x, if x were a sailor, then x is a soldier via universal biconditional elimination. From the fact that for all x, if x were a sailor, then x is a soldier, and that for all x, if x were a soldier, then x is a sailor we can infer that for all x, x is a sailor if and only if x is a soldier via universal biconditional introduction. Finally, from the fact that for all x, x is a sailor if and only if x is a soldier we can infer that for all x, if x were a sailor, then x is a soldier via universal biconditional elimination, which contradicts that There is at least one x for which the fact that x were a sailor does not imply that x is a soldier. Therefore, the answer is no.