Consider the following premises. For all x_4, if x_4 makes tea, then x_4 is not happy. William is cooking if and only if John is making tea. For all x_4, x_4 is happy. Can we infer the following from them? If we can, name the inference rule being used: William is not cooking.
 From the fact that for all x_4, if x_4 makes tea, then x_4 is not happy, and that for all x_4, x_4 is happy we can infer that for all x_4, x_4 will not make tea via universal modus tollens. From the fact that for all x_4, x_4 will not make tea we can infer that John is not making tea via universal instantiation. Finally, from the fact that William is cooking if and only if John is making tea, and that John is not making tea we can infer that William is not cooking via biconditional elimination. Therefore, the answer is yes.