Consider the following premises. For all x_6, if x_6 reads a book, then x_6 is a poet. For all x_6, if x_6 were a poet, then x_6 is climbing a mountain. Mary is reading a book. Can we infer the following from them? If we can, name the inference rule being used: Mary is climbing a mountain.
 From the fact that for all x_6, if x_6 reads a book, then x_6 is a poet, and that for all x_6, if x_6 were a poet, then x_6 is climbing a mountain we can infer that for all x_6, if x_6 reads a book, then x_6 is climbing a mountain via universal transitivity. From the fact that for all x_6, if x_6 reads a book, then x_6 is climbing a mountain we can infer that if Mary reads a book, then Mary is climbing a mountain via universal instantiation. Finally, from the fact that if Mary reads a book, then Mary is climbing a mountain, and that Mary is reading a book we can infer that Mary is climbing a mountain via modus ponens. Therefore, the answer is yes.