Consider the following premises. For all x_7, if x_7 makes tea, then x_7 is a doctor. For all x_7, x_7 will take a plane or x_7 will make tea. For all x_7, x_7 is rich. For all x_7, x_7 will take a plane if and only if x_7 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is rich and x_7 is a doctor.
 From the fact that for all x_7, x_7 will take a plane if and only if x_7 is a doctor we can infer that for all x_7, if x_7 takes a plane, then x_7 is a doctor via universal biconditional elimination. From the fact that for all x_7, if x_7 takes a plane, then x_7 is a doctor, that for all x_7, if x_7 makes tea, then x_7 is a doctor, and that for all x_7, x_7 will take a plane or x_7 will make tea we can infer that for all x_7, x_7 is a doctor via universal disjunction elimination. Finally, from the fact that for all x_7, x_7 is rich, and that for all x_7, x_7 is a doctor we can infer that for all x_7, x_7 is rich and x_7 is a doctor via universal conjunction. Therefore, the answer is yes.