Consider the following premises. For all x_1, if x_1 were an artist, then x_1 is an electrician. For all x_1, if x_1 were a scientist, then x_1 is an artist. There is at least one x_1 for which if x_1 were an electrician, then x_1 is a scientist. Can we infer the following from them? There is at least one x_1 for which x_1 is an electrician if and only if x_1 is a scientist.
 From the fact that for all x_1, if x_1 were a scientist, then x_1 is an artist, and that for all x_1, if x_1 were an artist, then x_1 is an electrician we can infer that for all x_1, if x_1 were a scientist, then x_1 is an electrician. Finally, from the fact that there is at least one x_1 for which if x_1 were an electrician, then x_1 is a scientist, and that for all x_1, if x_1 were a scientist, then x_1 is an electrician we can infer that there is at least one x_1 for which x_1 is an electrician if and only if x_1 is a scientist. Therefore, the answer is yes.