Consider the following premises. For all x_5, if x_5 were a lawyer, then x_5 is taking a plane. For all x_5, x_5 will take a plane if and only if x_5 is an astronaut. For all x_5, x_5 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not take a plane.
 From the fact that for all x_5, x_5 is a lawyer we can infer that for all x_5, x_5 is a lawyer or x_5 is an astronaut via universal addition. From the fact that for all x_5, x_5 will take a plane if and only if x_5 is an astronaut we can infer that for all x_5, if x_5 were an astronaut, then x_5 is taking a plane via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a lawyer, then x_5 is taking a plane, that for all x_5, if x_5 were an astronaut, then x_5 is taking a plane, and that for all x_5, x_5 is a lawyer or x_5 is an astronaut we can infer that for all x_5, x_5 will take a plane via universal disjunction elimination, which contradicts that There is at least one x_5 for which x_5 will not take a plane. Therefore, the answer is no.