Consider the following premises. David is taking a plane if and only if David is working. For all x_12, if x_12 works, then x_12 is taking a plane. David is not working. Can we infer the following from them? David is not taking a plane.
 From the fact that for all x_12, if x_12 works, then x_12 is taking a plane we can infer that if David works, then David is taking a plane. From the fact that David is taking a plane if and only if David is working we can infer that if David takes a plane, then David is working. From the fact that if David works, then David is taking a plane, and that if David takes a plane, then David is working we can infer that David is working if and only if David is taking a plane. Finally, from the fact that David is working if and only if David is taking a plane, and that David is not working we can infer that David is not taking a plane. Therefore, the answer is yes.