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_5, if x_5 were a police officer, then x_5 is writing a letter. There is at least one x_5 for which x_5 will write a letter or x_5 is a doctor. For all x_5, if x_5 were a doctor, then x_5 is a police officer. For all x_5, if x_5 writes a letter, then x_5 is a police officer.
For all x_5, if x_5 were a doctor, then x_5 is writing a letter can be inferred via the universal transitivity rule. There is at least one x_5 for which x_5 is a police officer can be inferred via the existential disjunction elimination rule. For all x_5, x_5 is a police officer if and only if x_5 will write a letter can be inferred via the universal biconditional introduction rule. For all x_5, x_5 will write a letter if and only if x_5 is a police officer can be inferred via the universal biconditional introduction rule.