Consider the following premises. For all x_9, if x_9 were fast, then x_9 is cooking. For all x_9, if x_9 cooks, then x_9 is fast. For all x_9, if x_9 cooks, then x_9 is climbing a mountain. There is at least one x_9 for which if x_9 were a musician, then x_9 is fast. 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 were a musician, then x_9 is climbing a mountain.
 From the fact that for all x_9, if x_9 cooks, then x_9 is fast, and that for all x_9, if x_9 were fast, then x_9 is cooking we can infer that for all x_9, x_9 will cook if and only if x_9 is fast via universal biconditional introduction. From the fact that for all x_9, x_9 will cook if and only if x_9 is fast we can infer that for all x_9, if x_9 were fast, then x_9 is cooking via universal biconditional elimination. From the fact that for all x_9, if x_9 were fast, then x_9 is cooking, and that for all x_9, if x_9 cooks, then x_9 is climbing a mountain we can infer that for all x_9, if x_9 were fast, then x_9 is climbing a mountain via universal transitivity. Finally, from the fact that there is at least one x_9 for which if x_9 were a musician, then x_9 is fast, and that for all x_9, if x_9 were fast, then x_9 is climbing a mountain we can infer that there is at least one x_9 for which if x_9 were a musician, then x_9 is climbing a mountain via existential transitivity. Therefore, the answer is yes.