Consider the following premises. For all y_1, y_1 is not fast. For all y_1, if y_1 were a taxi driver, then y_1 is an electrician. For all y_1, if y_1 were a taxi driver, then y_1 is fast. There is at least one y_1 for which if y_1 were a taxi driver, then y_1 is an electrician. For all y_1, if y_1 were an electrician, then y_1 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is not an electrician.
 From the fact that for all y_1, if y_1 were a taxi driver, then y_1 is an electrician, and that for all y_1, if y_1 were an electrician, then y_1 is a taxi driver we can infer that for all y_1, y_1 is a taxi driver if and only if y_1 is an electrician via universal biconditional introduction. From the fact that for all y_1, if y_1 were a taxi driver, then y_1 is fast, and that for all y_1, y_1 is not fast we can infer that for all y_1, y_1 is not a taxi driver via universal modus tollens. From the fact that for all y_1, y_1 is a taxi driver if and only if y_1 is an electrician we can infer that for all y_1, if y_1 were an electrician, then y_1 is a taxi driver via universal biconditional elimination. From the fact that there is at least one y_1 for which if y_1 were a taxi driver, then y_1 is an electrician, and that for all y_1, if y_1 were an electrician, then y_1 is a taxi driver we can infer that there is at least one y_1 for which y_1 is a taxi driver if and only if y_1 is an electrician via existential biconditional introduction. Finally, from the fact that there is at least one y_1 for which y_1 is a taxi driver if and only if y_1 is an electrician, and that for all y_1, y_1 is not a taxi driver we can infer that there is at least one y_1 for which y_1 is not an electrician via existential biconditional elimination. Therefore, the answer is yes.