Consider the following premises. For all x_5, if x_5 were a janitor, then x_5 is working. For all x_5, x_5 will make tea. For all x_5, if x_5 were fast, then x_5 is a janitor. For all x_5, x_5 is fast or x_5 is an astronaut. For all x_5, if x_5 were an astronaut, then x_5 is working. 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 will work.
 From the fact that for all x_5, if x_5 were fast, then x_5 is a janitor, and that for all x_5, if x_5 were a janitor, then x_5 is working we can infer that for all x_5, if x_5 were fast, then x_5 is working via universal transitivity. From the fact that for all x_5, if x_5 were fast, then x_5 is working, that for all x_5, if x_5 were an astronaut, then x_5 is working, and that for all x_5, x_5 is fast or x_5 is an astronaut we can infer that for all x_5, x_5 will work 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 will work we can infer that for all x_5, x_5 will make tea and x_5 will work via universal conjunction. Therefore, the answer is yes.