Consider the following premises. For all z_2, z_2 is an astronaut or z_2 is not an electrician. For all z_2, if z_2 were an electrician, then z_2 is a doctor. For all z_2, if z_2 were a doctor, then z_2 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_2 for which the fact that z_2 were a doctor does not imply that z_2 is an astronaut.
 From the fact that for all z_2, z_2 is an astronaut or z_2 is not an electrician we can infer that for all z_2, if z_2 were an electrician, then z_2 is an astronaut via universal rewriting. From the fact that for all z_2, if z_2 were a doctor, then z_2 is an electrician, and that for all z_2, if z_2 were an electrician, then z_2 is a doctor we can infer that for all z_2, z_2 is a doctor if and only if z_2 is an electrician via universal biconditional introduction. From the fact that for all z_2, z_2 is a doctor if and only if z_2 is an electrician we can infer that for all z_2, if z_2 were a doctor, then z_2 is an electrician via universal biconditional elimination. Finally, from the fact that for all z_2, if z_2 were a doctor, then z_2 is an electrician, and that for all z_2, if z_2 were an electrician, then z_2 is an astronaut we can infer that for all z_2, if z_2 were a doctor, then z_2 is an astronaut via universal transitivity, which contradicts that There is at least one z_2 for which the fact that z_2 were a doctor does not imply that z_2 is an astronaut. Therefore, the answer is no.