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_8, if x_8 were a doctor, then x_8 is a nurse. For all x_8, if x_8 were a janitor, then x_8 is a nurse. For all x_8, if x_8 plays a game, then x_8 is not a nurse. For all x_8, x_8 will play a game if and only if x_8 will write a letter. For all x_8, x_8 is a janitor or x_8 is a doctor.
For all x_8, x_8 is a nurse can be inferred via the universal disjunction elimination rule. For all x_8, if x_8 plays a game, then x_8 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 writes a letter, then x_8 is playing a game can be inferred via the universal biconditional elimination rule.