Consider the following premises. Joseph is not making tea. For all x_7, if x_7 cooks, then x_7 is making tea. For all x_7, x_7 will cook if and only if x_7 will make tea. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not cooking.
 From the fact that for all x_7, x_7 will cook if and only if x_7 will make tea we can infer that for all x_7, if x_7 makes tea, then x_7 is cooking via universal biconditional elimination. From the fact that for all x_7, if x_7 cooks, then x_7 is making tea, and that for all x_7, if x_7 makes tea, then x_7 is cooking we can infer that for all x_7, x_7 will cook if and only if x_7 will make tea via universal biconditional introduction. From the fact that for all x_7, x_7 will cook if and only if x_7 will make tea we can infer that Joseph is cooking if and only if Joseph is making tea via universal instantiation. Finally, from the fact that Joseph is cooking if and only if Joseph is making tea, and that Joseph is not making tea we can infer that Joseph is not cooking via biconditional elimination. Therefore, the answer is yes.