Consider the following premises. For all x_7, x_7 is an electrician if and only if x_7 will cook. If Sarah were an electrician, then Thomas is a writer. Thomas is not a writer. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not cooking.
 From the fact that for all x_7, x_7 is an electrician if and only if x_7 will cook we can infer that Sarah is an electrician if and only if Sarah is cooking via universal instantiation. From the fact that if Sarah were an electrician, then Thomas is a writer, and that Thomas is not a writer we can infer that Sarah is not an electrician via modus tollens. Finally, from the fact that Sarah is an electrician if and only if Sarah is cooking, and that Sarah is not an electrician we can infer that Sarah is not cooking via biconditional elimination. Therefore, the answer is yes.