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_3, if z_3 were poor, then z_3 is an astronaut. For all z_3, if z_3 were an astronaut, then z_3 is poor. For all z_3, z_3 is not an astronaut. For all z_3, if z_3 were poor, then z_3 is an astronaut.
For all z_3, z_3 is not poor can be inferred via the universal modus tollens rule. For all z_3, z_3 is not poor can be inferred via the universal modus tollens rule. For all z_3, z_3 is poor if and only if z_3 is an astronaut can be inferred via the universal biconditional introduction rule. For all z_3, z_3 is an astronaut if and only if z_3 is poor can be inferred via the universal biconditional introduction rule. For all z_3, z_3 is an astronaut if and only if z_3 is poor can be inferred via the universal biconditional introduction rule. For all z_3, z_3 is poor if and only if z_3 is an astronaut can be inferred via the universal biconditional introduction rule.