Consider the following premises. For all x_6, x_6 is excited. For all x_6, x_6 will climb a mountain. For all x_6, if x_6 were a writer, then x_6 is making tea. For all x_6, x_6 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will make tea and x_6 is excited.
 From the fact that for all x_6, if x_6 were a writer, then x_6 is making tea, and that for all x_6, x_6 is a writer we can infer that for all x_6, x_6 will make tea via universal modus ponens. From the fact that for all x_6, x_6 will make tea, and that for all x_6, x_6 will climb a mountain we can infer that for all x_6, x_6 will make tea and x_6 will climb a mountain via universal conjunction. From the fact that for all x_6, x_6 will make tea and x_6 will climb a mountain we can infer that for all x_6, x_6 will make tea via universal simplification. Finally, from the fact that for all x_6, x_6 will make tea, and that for all x_6, x_6 is excited we can infer that for all x_6, x_6 will make tea and x_6 is excited via universal conjunction. Therefore, the answer is yes.