Consider the following premises. For all x_5, if x_5 were a nurse, then x_5 is a bartender. For all x_5, x_5 is a nurse or x_5 is not a bartender. Can we infer the following from them? If Jennifer were a bartender, then Jennifer is a nurse.
 From the fact that for all x_5, x_5 is a nurse or x_5 is not a bartender we can infer that for all x_5, if x_5 were a bartender, then x_5 is a nurse. From the fact that for all x_5, if x_5 were a nurse, then x_5 is a bartender, and that for all x_5, if x_5 were a bartender, then x_5 is a nurse we can infer that for all x_5, x_5 is a nurse if and only if x_5 is a bartender. From the fact that for all x_5, x_5 is a nurse if and only if x_5 is a bartender we can infer that Jennifer is a nurse if and only if Jennifer is a bartender. Finally, from the fact that Jennifer is a nurse if and only if Jennifer is a bartender we can infer that if Jennifer were a bartender, then Jennifer is a nurse. Therefore, the answer is yes.