Consider the following premises. For all z, if z were fast, then z is playing tennis. For all z, z is fast 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 the fact that z plays tennis does not imply that z is fast.
 From the fact that for all z, z is fast if and only if z will play tennis we can infer that for all z, if z plays tennis, then z is fast via universal biconditional elimination. From the fact that for all z, if z were fast, then z is playing tennis, and that for all z, if z plays tennis, then z is fast we can infer that for all z, z is fast if and only if z will play tennis via universal biconditional introduction. Finally, from the fact that for all z, z is fast if and only if z will play tennis we can infer that for all z, if z plays tennis, then z is fast via universal biconditional elimination, which contradicts that There is at least one z for which the fact that z plays tennis does not imply that z is fast. Therefore, the answer is no.