Consider the following premises. For all z, z will climb a mountain or z is not a musician. There is at least one z for which z is a musician if and only if z will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if z plays tennis, then z is climbing a mountain.
 From the fact that for all z, z will climb a mountain or z is not a musician we can infer that for all z, if z were a musician, then z is climbing a mountain via universal rewriting. From the fact that there is at least one z for which z is a musician if and only if z will play tennis we can infer that there is at least one z for which if z plays tennis, then z is a musician via existential biconditional elimination. Finally, from the fact that there is at least one z for which if z plays tennis, then z is a musician, and that for all z, if z were a musician, then z is climbing a mountain we can infer that there is at least one z for which if z plays tennis, then z is climbing a mountain via existential transitivity. Therefore, the answer is yes.