Consider the following premises. For all x_13, if x_13 makes tea, then x_13 is a poet. If Charles were a writer, then Charles is making tea. For all x_13, if x_13 were a poet, then x_13 is a writer. Charles is a writer. Can we infer the following from them? If we can, name the inference rule being used: Charles is making tea.
 From the fact that for all x_13, if x_13 makes tea, then x_13 is a poet, and that for all x_13, if x_13 were a poet, then x_13 is a writer we can infer that for all x_13, if x_13 makes tea, then x_13 is a writer via universal transitivity. From the fact that for all x_13, if x_13 makes tea, then x_13 is a writer we can infer that if Charles makes tea, then Charles is a writer via universal instantiation. From the fact that if Charles were a writer, then Charles is making tea, and that if Charles makes tea, then Charles is a writer we can infer that Charles is a writer if and only if Charles is making tea via biconditional introduction. From the fact that Charles is a writer if and only if Charles is making tea we can infer that if Charles were a writer, then Charles is making tea via biconditional elimination. Finally, from the fact that if Charles were a writer, then Charles is making tea, and that Charles is a writer we can infer that Charles is making tea via modus ponens. Therefore, the answer is yes.