Consider the following premises. For all z, z will not cook. Thomas is an astronaut if and only if Barbara is cooking. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not an astronaut.
 From the fact that for all z, z will not cook we can infer that Barbara is not cooking via universal instantiation. Finally, from the fact that Thomas is an astronaut if and only if Barbara is cooking, and that Barbara is not cooking we can infer that Thomas is not an astronaut via biconditional elimination. Therefore, the answer is yes.