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_11, x_11 is a nurse if and only if x_11 is a bartender. James is not driving a car. Charles is not a bartender. For all x_22, x_22 will play a game if and only if x_22 will drive a car.
James is not driving a car and Charles is not a bartender can be inferred via the conjunction rule. Charles is not a bartender and James is not driving a car can be inferred via the conjunction rule. For all x_11, if x_11 were a nurse, then x_11 is a bartender can be inferred via the universal biconditional elimination rule. For all x_22, if x_22 plays a game, then x_22 is driving a car can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 were a bartender, then x_11 is a nurse can be inferred via the universal biconditional elimination rule. For all x_22, if x_22 drives a car, then x_22 is playing a game can be inferred via the universal biconditional elimination rule.