Consider the following premises. For all x_6, if x_6 were a soldier, then x_6 is writing a letter. For all x_6, if x_6 writes a letter, then x_6 is a soldier. There is at least one x_6 for which if x_6 were a soldier, then x_6 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if is not true that x_6 will write a letter if and only if x_6 is a soldier.
 From the fact that there is at least one x_6 for which if x_6 were a soldier, then x_6 is writing a letter, and that for all x_6, if x_6 writes a letter, then x_6 is a soldier we can infer that there is at least one x_6 for which x_6 is a soldier if and only if x_6 will write a letter via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 is a soldier if and only if x_6 will write a letter we can infer that there is at least one x_6 for which if x_6 writes a letter, then x_6 is a soldier via existential biconditional elimination. Finally, from the fact that there is at least one x_6 for which if x_6 writes a letter, then x_6 is a soldier, and that for all x_6, if x_6 were a soldier, then x_6 is writing a letter we can infer that there is at least one x_6 for which x_6 will write a letter if and only if x_6 is a soldier via existential biconditional introduction, which contradicts that For all x_6, if is not true that x_6 will write a letter if and only if x_6 is a soldier. Therefore, the answer is no.