Consider the following premises. There is at least one x_9 for which x_9 will climb a mountain if and only if x_9 will make tea. For all x_9, x_9 will read a book if and only if x_9 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which if x_9 makes tea, then x_9 is reading a book.
 From the fact that for all x_9, x_9 will read a book if and only if x_9 will climb a mountain we can infer that for all x_9, if x_9 climbs a mountain, then x_9 is reading a book via universal biconditional elimination. From the fact that there is at least one x_9 for which x_9 will climb a mountain if and only if x_9 will make tea we can infer that there is at least one x_9 for which if x_9 makes tea, then x_9 is climbing a mountain via existential biconditional elimination. Finally, from the fact that there is at least one x_9 for which if x_9 makes tea, then x_9 is climbing a mountain, and that for all x_9, if x_9 climbs a mountain, then x_9 is reading a book we can infer that there is at least one x_9 for which if x_9 makes tea, then x_9 is reading a book via existential transitivity. Therefore, the answer is yes.