Consider the following premises. For all x_11, x_11 will play squash if and only if x_11 will cook. Joseph is not playing squash. If it rains, then Joseph is cooking. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_11, x_11 will play squash if and only if x_11 will cook we can infer that Joseph is playing squash if and only if Joseph is cooking via universal instantiation. From the fact that Joseph is playing squash if and only if Joseph is cooking, and that Joseph is not playing squash we can infer that Joseph is not cooking via biconditional elimination. Finally, from the fact that if it rains, then Joseph is cooking, and that Joseph is not cooking we can infer that it is not raining via modus tollens. Therefore, the answer is yes.