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 z_1, z_1 is an astronaut if and only if z_1 is a cashier. For all z_1, if z_1 were a cashier, then z_1 is an astronaut. For all z_1, if z_1 were an astronaut, then z_1 is a cashier.
For all z_1, z_1 is a cashier if and only if z_1 is an astronaut can be inferred via the universal biconditional introduction rule. For all z_1, z_1 is an astronaut if and only if z_1 is a cashier can be inferred via the universal biconditional introduction rule. For all z_1, if z_1 were an astronaut, then z_1 is a cashier can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were a cashier, then z_1 is an astronaut can be inferred via the universal biconditional elimination rule.