Consider the following premises. For all x_7, x_7 is an electrician if and only if x_7 is a police officer. For all x_7, x_7 is a mechanic if and only if x_7 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which the fact that x_7 were an electrician does not imply that x_7 is a mechanic.
 From the fact that for all x_7, x_7 is an electrician if and only if x_7 is a police officer we can infer that for all x_7, if x_7 were an electrician, then x_7 is a police officer via universal biconditional elimination. From the fact that for all x_7, x_7 is a mechanic if and only if x_7 is a police officer we can infer that for all x_7, if x_7 were a police officer, then x_7 is a mechanic via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 were an electrician, then x_7 is a police officer, and that for all x_7, if x_7 were a police officer, then x_7 is a mechanic we can infer that for all x_7, if x_7 were an electrician, then x_7 is a mechanic via universal transitivity, which contradicts that There is at least one x_7 for which the fact that x_7 were an electrician does not imply that x_7 is a mechanic. Therefore, the answer is no.