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 a carpenter if and only if z_1 is a doctor. For all z_1, if z_1 were a carpenter, then z_1 is a bartender. For all z_1, z_1 is not a doctor. For all z_1, z_1 is a carpenter if and only if z_1 is a bartender.
For all z_1, if z_1 were a carpenter, then z_1 is a doctor can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were a carpenter, then z_1 is a bartender can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were a doctor, then z_1 is a carpenter can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were a bartender, then z_1 is a carpenter can be inferred via the universal biconditional elimination rule. For all z_1, z_1 is not a carpenter can be inferred via the universal biconditional elimination rule.