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 y_1, y_1 is a lawyer if and only if y_1 is a carpenter. For all y_1, if y_1 were a lawyer, then y_1 is a taxi driver. There is at least one y_1 for which y_1 is not a lawyer. For all y_1, if y_1 were a taxi driver, then y_1 is a carpenter.
For all y_1, if y_1 were a lawyer, then y_1 is a carpenter can be inferred via the universal transitivity rule. For all y_1, if y_1 were a lawyer, then y_1 is a carpenter can be inferred via the universal biconditional elimination rule. For all y_1, if y_1 were a carpenter, then y_1 is a lawyer can be inferred via the universal biconditional elimination rule. There is at least one y_1 for which y_1 is not a carpenter can be inferred via the existential biconditional elimination rule.