Consider the following premises. For all z, z is an artist if and only if z will play squash. For all z, z is a nurse or z will play squash. There is at least one z for which z is an artist if and only if z is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is not an artist.
 From the fact that for all z, z is an artist if and only if z will play squash we can infer that for all z, if z plays squash, then z is an artist via universal biconditional elimination. From the fact that there is at least one z for which z is an artist if and only if z is a nurse we can infer that there is at least one z for which if z were a nurse, then z is an artist via existential biconditional elimination. Finally, from the fact that there is at least one z for which if z were a nurse, then z is an artist, that for all z, if z plays squash, then z is an artist, and that for all z, z is a nurse or z will play squash we can infer that there is at least one z for which z is an artist via existential disjunction elimination, which contradicts that For all z, z is not an artist. Therefore, the answer is no.