Consider the following premises. For all z, z is a mechanic or z is not an office clerk. For all z, if z were a mechanic, then z is an office clerk. 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 is not true that z is an office clerk if and only if z is a mechanic.
 From the fact that for all z, z is a mechanic or z is not an office clerk we can infer that for all z, if z were an office clerk, then z is a mechanic via universal rewriting. Finally, from the fact that for all z, if z were an office clerk, then z is a mechanic, and that for all z, if z were a mechanic, then z is an office clerk we can infer that for all z, z is an office clerk if and only if z is a mechanic via universal biconditional introduction, which contradicts that There is at least one z for which if is not true that z is an office clerk if and only if z is a mechanic. Therefore, the answer is no.