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, if z were poor, then z is taking a plane. For all z, z is not an office clerk. For all z, z is an office clerk if and only if z is poor. There is at least one z for which z will take a plane if and only if z is a carpenter. For all z, if z takes a plane, then z is poor.
For all z, z is poor if and only if z will take a plane can be inferred via the universal biconditional introduction rule. For all z, z will take a plane if and only if z is poor can be inferred via the universal biconditional introduction rule. For all z, if z were an office clerk, then z is poor can be inferred via the universal biconditional elimination rule. There is at least one z for which if z takes a plane, then z is a carpenter can be inferred via the existential biconditional elimination rule. For all z, if z were poor, then z is an office clerk can be inferred via the universal biconditional elimination rule. There is at least one z for which if z were a carpenter, then z is taking a plane can be inferred via the existential biconditional elimination rule. For all z, z is not poor can be inferred via the universal biconditional elimination rule.