Consider the following premises. There is at least one x_16 for which x_16 will sleep if and only if x_16 is a nurse. For all x_16, if x_16 were happy, then x_16 is a nurse. For all x_16, if x_16 sleeps, then x_16 is writing a letter. For all x_16, if x_16 writes a letter, then x_16 is happy. Can we infer the following from them? There is at least one x_16 for which if x_16 writes a letter, then x_16 is a nurse.
 From the fact that there is at least one x_16 for which x_16 will sleep if and only if x_16 is a nurse we can infer that there is at least one x_16 for which if x_16 were a nurse, then x_16 is sleeping. From the fact that for all x_16, if x_16 writes a letter, then x_16 is happy, and that for all x_16, if x_16 were happy, then x_16 is a nurse we can infer that for all x_16, if x_16 writes a letter, then x_16 is a nurse. From the fact that there is at least one x_16 for which if x_16 were a nurse, then x_16 is sleeping, and that for all x_16, if x_16 sleeps, then x_16 is writing a letter we can infer that there is at least one x_16 for which if x_16 were a nurse, then x_16 is writing a letter. From the fact that there is at least one x_16 for which if x_16 were a nurse, then x_16 is writing a letter, and that for all x_16, if x_16 writes a letter, then x_16 is a nurse we can infer that there is at least one x_16 for which x_16 is a nurse if and only if x_16 will write a letter. Finally, from the fact that there is at least one x_16 for which x_16 is a nurse if and only if x_16 will write a letter we can infer that there is at least one x_16 for which if x_16 writes a letter, then x_16 is a nurse. Therefore, the answer is yes.