Consider the following premises. For all z, if z were a nurse, then z is an electrician. For all z, z is an electrician or z is an astronaut. There is at least one z for which if z were an astronaut, then z is a nurse. For all z, if z were an electrician, then 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 a nurse.
 From the fact that for all z, if z were an electrician, then z is a nurse, and that for all z, if z were a nurse, then z is an electrician we can infer that for all z, z is an electrician if and only if z is a nurse via universal biconditional introduction. From the fact that for all z, z is an electrician if and only if z is a nurse we can infer that for all z, if z were an electrician, then z is a nurse via universal biconditional elimination. Finally, from the fact that for all z, if z were an electrician, then z is a nurse, that there is at least one z for which if z were an astronaut, then z is a nurse, and that for all z, z is an electrician or z is an astronaut we can infer that there is at least one z for which z is a nurse via existential disjunction elimination, which contradicts that For all z, z is not a nurse. Therefore, the answer is no.