Consider the following premises. For all x_3, x_3 is a doctor or x_3 is not an electrician. For all x_3, x_3 is a doctor if and only if x_3 is an electrician. For all x_3, x_3 is not an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is a doctor.
 From the fact that for all x_3, x_3 is a doctor or x_3 is not an electrician we can infer that for all x_3, if x_3 were an electrician, then x_3 is a doctor via universal rewriting. From the fact that for all x_3, x_3 is a doctor if and only if x_3 is an electrician we can infer that for all x_3, if x_3 were a doctor, then x_3 is an electrician via universal biconditional elimination. From the fact that for all x_3, if x_3 were an electrician, then x_3 is a doctor, and that for all x_3, if x_3 were a doctor, then x_3 is an electrician we can infer that for all x_3, x_3 is an electrician if and only if x_3 is a doctor via universal biconditional introduction. Finally, from the fact that for all x_3, x_3 is an electrician if and only if x_3 is a doctor, and that for all x_3, x_3 is not an electrician we can infer that for all x_3, x_3 is not a doctor via universal biconditional elimination, which contradicts that There is at least one x_3 for which x_3 is a doctor. Therefore, the answer is no.