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, x_10 is not a politician. For all x_10, if x_10 were a taxi driver, then x_10 is a politician. For all x_10, if x_10 plays tennis, then x_10 is an office clerk. For all x_10, x_10 is a taxi driver or x_10 will not play tennis. For all x_10, if x_10 were an office clerk, then x_10 is playing tennis.
For all x_10, x_10 is not a taxi driver can be inferred via the universal modus tollens rule. For all x_10, if x_10 plays tennis, then x_10 is a taxi driver can be inferred via the universal rewriting rule. For all x_10, x_10 will play tennis if and only if x_10 is an office clerk can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is an office clerk if and only if x_10 will play tennis can be inferred via the universal biconditional introduction rule.