Consider the following premises. For all x_5, x_5 is a police officer if and only if x_5 is sad. For all x_5, x_5 is sad. For all x_5, if x_5 listens to a song, then x_5 is a police officer. Can we infer the following from them? For all x_5, x_5 is a police officer.
 From the fact that for all x_5, x_5 is sad we can infer that for all x_5, x_5 is sad or x_5 will listen to a song. From the fact that for all x_5, x_5 is a police officer if and only if x_5 is sad we can infer that for all x_5, if x_5 were sad, then x_5 is a police officer. Finally, from the fact that for all x_5, if x_5 were sad, then x_5 is a police officer, that for all x_5, if x_5 listens to a song, then x_5 is a police officer, and that for all x_5, x_5 is sad or x_5 will listen to a song we can infer that for all x_5, x_5 is a police officer. Therefore, the answer is yes.