What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x_10, if x_10 were a politician, then x_10 is not writing a letter. For all x_10, if x_10 goes running, then x_10 is taking a plane. For all x_10, x_10 will write a letter. There is at least one x_10 for which x_10 is a politician if and only if x_10 will take a plane.
For all x_10, x_10 is not a politician can be inferred via the universal modus tollens rule. There is at least one x_10 for which if x_10 were a politician, then x_10 is taking a plane can be inferred via the existential biconditional elimination rule. There is at least one x_10 for which if x_10 takes a plane, then x_10 is a politician can be inferred via the existential biconditional elimination rule.