Consider the following premises. For all x_6, x_6 will not make tea. There is at least one x_6 for which if x_6 cooks, then x_6 is making tea. For all x_6, x_6 will cook if and only if x_6 will make tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not cook.
 From the fact that for all x_6, x_6 will cook if and only if x_6 will make tea we can infer that for all x_6, if x_6 makes tea, then x_6 is cooking via universal biconditional elimination. From the fact that for all x_6, if x_6 makes tea, then x_6 is cooking, and that there is at least one x_6 for which if x_6 cooks, then x_6 is making tea we can infer that there is at least one x_6 for which x_6 will make tea if and only if x_6 will cook via existential biconditional introduction. Finally, from the fact that there is at least one x_6 for which x_6 will make tea if and only if x_6 will cook, and that for all x_6, x_6 will not make tea we can infer that there is at least one x_6 for which x_6 will not cook via existential biconditional elimination. Therefore, the answer is yes.