Consider the following premises. For all x_10, if x_10 were a politician, then x_10 is playing tennis. For all x_10, if x_10 were a poet, then x_10 is taking a plane. For all x_10, if x_10 plays tennis, then x_10 is a politician. For all x_10, if x_10 takes a plane, then x_10 is playing tennis. For all x_10, x_10 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a politician.
 From the fact that for all x_10, if x_10 were a poet, then x_10 is taking a plane, and that for all x_10, if x_10 takes a plane, then x_10 is playing tennis we can infer that for all x_10, if x_10 were a poet, then x_10 is playing tennis via universal transitivity. From the fact that for all x_10, if x_10 were a politician, then x_10 is playing tennis, and that for all x_10, if x_10 plays tennis, then x_10 is a politician we can infer that for all x_10, x_10 is a politician if and only if x_10 will play tennis via universal biconditional introduction. From the fact that for all x_10, x_10 is a politician if and only if x_10 will play tennis we can infer that for all x_10, if x_10 plays tennis, then x_10 is a politician via universal biconditional elimination. From the fact that for all x_10, if x_10 were a poet, then x_10 is playing tennis, and that for all x_10, if x_10 plays tennis, then x_10 is a politician we can infer that for all x_10, if x_10 were a poet, then x_10 is a politician via universal transitivity. Finally, from the fact that for all x_10, if x_10 were a poet, then x_10 is a politician, and that for all x_10, x_10 is a poet we can infer that for all x_10, x_10 is a politician via universal modus ponens. Therefore, the answer is yes.