Consider the following premises. For all x_1, if x_1 were an electrician, then x_1 is a bartender. For all x_1, if x_1 were a bartender, then x_1 is a scientist. There is at least one x_1 for which if x_1 were a scientist, then x_1 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_1 for which x_1 is a scientist if and only if x_1 is a bartender.
 From the fact that there is at least one x_1 for which if x_1 were a scientist, then x_1 is an electrician, and that for all x_1, if x_1 were an electrician, then x_1 is a bartender we can infer that there is at least one x_1 for which if x_1 were a scientist, then x_1 is a bartender via existential transitivity. Finally, from the fact that there is at least one x_1 for which if x_1 were a scientist, then x_1 is a bartender, and that for all x_1, if x_1 were a bartender, then x_1 is a scientist we can infer that there is at least one x_1 for which x_1 is a scientist if and only if x_1 is a bartender via existential biconditional introduction. Therefore, the answer is yes.