Consider the following premises. For all x_5, if x_5 drives a car, then x_5 is listening to a song. For all x_5, if x_5 listens to a song, then x_5 is a doctor. For all x_5, x_5 will make tea. For all x_5, x_5 will drive a car or x_5 is a writer. For all x_5, if x_5 were a writer, then x_5 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will make tea and x_5 is a doctor.
 From the fact that for all x_5, if x_5 drives a car, then x_5 is listening to a song, and that for all x_5, if x_5 listens to a song, then x_5 is a doctor we can infer that for all x_5, if x_5 drives a car, then x_5 is a doctor via universal transitivity. From the fact that for all x_5, if x_5 drives a car, then x_5 is a doctor, that for all x_5, if x_5 were a writer, then x_5 is a doctor, and that for all x_5, x_5 will drive a car or x_5 is a writer we can infer that for all x_5, x_5 is a doctor via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will make tea, and that for all x_5, x_5 is a doctor we can infer that for all x_5, x_5 will make tea and x_5 is a doctor via universal conjunction. Therefore, the answer is yes.