Consider the following premises. For all z, z is not a nurse. If Barbara were a musician, then Michael is a nurse. For all z_4, if z_4 takes a plane, then z_4 is a musician. For all z_4, if z_4 were a musician, then z_4 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not taking a plane.
 From the fact that for all z_4, if z_4 takes a plane, then z_4 is a musician, and that for all z_4, if z_4 were a musician, then z_4 is taking a plane we can infer that for all z_4, z_4 will take a plane if and only if z_4 is a musician via universal biconditional introduction. From the fact that for all z_4, z_4 will take a plane if and only if z_4 is a musician we can infer that Barbara is taking a plane if and only if Barbara is a musician via universal instantiation. From the fact that for all z, z is not a nurse we can infer that Michael is not a nurse via universal instantiation. From the fact that if Barbara were a musician, then Michael is a nurse, and that Michael is not a nurse we can infer that Barbara is not a musician via modus tollens. Finally, from the fact that Barbara is taking a plane if and only if Barbara is a musician, and that Barbara is not a musician we can infer that Barbara is not taking a plane via biconditional elimination. Therefore, the answer is yes.