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_12, x_12 is rich. For all x_12, x_12 is a carpenter if and only if x_12 is rich. For all x_12, if x_12 were a carpenter, then x_12 is an astronaut. For all x_12, if x_12 were an astronaut, then x_12 is driving a car.
For all x_12, if x_12 were a carpenter, then x_12 is driving a car can be inferred via the universal transitivity rule. For all x_12, if x_12 were a carpenter, then x_12 is rich can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were rich, then x_12 is a carpenter can be inferred via the universal biconditional elimination rule.