Consider the following premises. There is at least one z for which z will climb a mountain if and only if z is a taxi driver. For all z, z is not a musician. For all z, z is a musician if and only if z 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 z for which z is not a taxi driver.
 From the fact that for all z, z is a musician if and only if z will climb a mountain, and that for all z, z is not a musician we can infer that for all z, z will not climb a mountain via universal biconditional elimination. Finally, from the fact that there is at least one z for which z will climb a mountain if and only if z is a taxi driver, and that for all z, z will not climb a mountain we can infer that there is at least one z for which z is not a taxi driver via existential biconditional elimination. Therefore, the answer is yes.