Consider the following premises. For all x_13, if x_13 drinks water, then x_13 is rich. For all x_13, if x_13 makes tea, then x_13 is a writer. For all x_13, x_13 will make tea or x_13 is not rich. For all x_13, if x_13 were a writer, then x_13 is making tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, if x_13 drinks water, then x_13 is a writer.
 From the fact that for all x_13, if x_13 were a writer, then x_13 is making tea, and that for all x_13, if x_13 makes tea, then x_13 is a writer we can infer that for all x_13, x_13 is a writer if and only if x_13 will make tea via universal biconditional introduction. From the fact that for all x_13, x_13 is a writer if and only if x_13 will make tea we can infer that for all x_13, if x_13 makes tea, then x_13 is a writer via universal biconditional elimination. From the fact that for all x_13, x_13 will make tea or x_13 is not rich we can infer that for all x_13, if x_13 were rich, then x_13 is making tea via universal rewriting. From the fact that for all x_13, if x_13 drinks water, then x_13 is rich, and that for all x_13, if x_13 were rich, then x_13 is making tea we can infer that for all x_13, if x_13 drinks water, then x_13 is making tea via universal transitivity. Finally, from the fact that for all x_13, if x_13 drinks water, then x_13 is making tea, and that for all x_13, if x_13 makes tea, then x_13 is a writer we can infer that for all x_13, if x_13 drinks water, then x_13 is a writer via universal transitivity. Therefore, the answer is yes.