Consider the following premises. For all z_3, if z_3 were a mechanic, then z_3 is a scientist. Joseph is not a scientist. For all z_3, z_3 is a mechanic or z_3 is not a scientist. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not a mechanic.
 From the fact that for all z_3, z_3 is a mechanic or z_3 is not a scientist we can infer that for all z_3, if z_3 were a scientist, then z_3 is a mechanic via universal rewriting. From the fact that for all z_3, if z_3 were a scientist, then z_3 is a mechanic, and that for all z_3, if z_3 were a mechanic, then z_3 is a scientist we can infer that for all z_3, z_3 is a scientist if and only if z_3 is a mechanic via universal biconditional introduction. From the fact that for all z_3, z_3 is a scientist if and only if z_3 is a mechanic we can infer that Joseph is a scientist if and only if Joseph is a mechanic via universal instantiation. Finally, from the fact that Joseph is a scientist if and only if Joseph is a mechanic, and that Joseph is not a scientist we can infer that Joseph is not a mechanic via biconditional elimination. Therefore, the answer is yes.