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