Consider the following premises. For all x_3, x_3 is a doctor or x_3 is not happy. For all x_3, if x_3 were a doctor, then x_3 is driving a car. For all x_3, if x_3 drives a car, then x_3 is happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which the fact that x_3 were a doctor does not imply that x_3 is happy.
 From the fact that for all x_3, if x_3 were a doctor, then x_3 is driving a car, and that for all x_3, if x_3 drives a car, then x_3 is happy we can infer that for all x_3, if x_3 were a doctor, then x_3 is happy via universal transitivity. From the fact that for all x_3, x_3 is a doctor or x_3 is not happy we can infer that for all x_3, if x_3 were happy, then x_3 is a doctor via universal rewriting. From the fact that for all x_3, if x_3 were a doctor, then x_3 is happy, and that for all x_3, if x_3 were happy, then x_3 is a doctor we can infer that for all x_3, x_3 is a doctor if and only if x_3 is happy via universal biconditional introduction. Finally, from the fact that for all x_3, x_3 is a doctor if and only if x_3 is happy we can infer that for all x_3, if x_3 were a doctor, then x_3 is happy via universal biconditional elimination, which contradicts that There is at least one x_3 for which the fact that x_3 were a doctor does not imply that x_3 is happy. Therefore, the answer is no.