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 sad. For all z_1, z_1 is a carpenter if and only if z_1 will drive a car. For all z_1, z_1 will not drive a car. For all z_1, if z_1 were a carpenter, then z_1 is sad.
For all z_1, if z_1 were a carpenter, then z_1 is sad can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were a carpenter, then z_1 is driving a car can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 were sad, then z_1 is a carpenter can be inferred via the universal biconditional elimination rule. For all z_1, if z_1 drives a car, 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.