Consider the following premises. For all x_5, if x_5 writes a letter, then x_5 is a soldier. For all x_5, if x_5 were a soldier, then x_5 is working. For all x_5, if x_5 drinks water, then x_5 is writing a letter. For all x_5, if x_5 works, then x_5 is drinking water. Can we infer the following from them? There is at least one x_5 for which if is not true that x_5 will drink water if and only if x_5 will write a letter.
 From the fact that for all x_5, if x_5 were a soldier, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is drinking water we can infer that for all x_5, if x_5 were a soldier, then x_5 is drinking water. From the fact that for all x_5, if x_5 writes a letter, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, then x_5 is drinking water we can infer that for all x_5, if x_5 writes a letter, then x_5 is drinking water. Finally, from the fact that for all x_5, if x_5 drinks water, then x_5 is writing a letter, and that for all x_5, if x_5 writes a letter, then x_5 is drinking water we can infer that for all x_5, x_5 will drink water if and only if x_5 will write a letter, which contradicts that There is at least one x_5 for which if is not true that x_5 will drink water if and only if x_5 will write a letter. Therefore, the answer is no.