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: There is at least one z_4 for which z_4 is a doctor if and only if z_4 is a politician. For all z_4, z_4 will make tea if and only if z_4 is a politician. For all z_4, z_4 will take a plane if and only if z_4 will make tea. For all z_4, z_4 is not a doctor.
For all z_4, if z_4 makes tea, then z_4 is a politician can be inferred via the universal biconditional elimination rule. For all z_4, if z_4 takes a plane, then z_4 is making tea can be inferred via the universal biconditional elimination rule. There is at least one z_4 for which if z_4 were a doctor, then z_4 is a politician can be inferred via the existential biconditional elimination rule. For all z_4, if z_4 were a politician, then z_4 is making tea can be inferred via the universal biconditional elimination rule. For all z_4, if z_4 makes tea, then z_4 is taking a plane can be inferred via the universal biconditional elimination rule. There is at least one z_4 for which if z_4 were a politician, then z_4 is a doctor can be inferred via the existential biconditional elimination rule. There is at least one z_4 for which z_4 is not a politician can be inferred via the existential biconditional elimination rule.