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_2, y_2 is not an astronaut. There is at least one y_2 for which if y_2 were a doctor, then y_2 is a writer. For all y_2, y_2 is a doctor or y_2 is not fast. For all y_2, if y_2 were a writer, then y_2 is fast. For all y_2, y_2 is a doctor if and only if y_2 is an astronaut.
There is at least one y_2 for which if y_2 were a doctor, then y_2 is fast can be inferred via the existential transitivity rule. For all y_2, if y_2 were fast, then y_2 is a doctor can be inferred via the universal rewriting rule. For all y_2, if y_2 were a doctor, then y_2 is an astronaut can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 were an astronaut, then y_2 is a doctor can be inferred via the universal biconditional elimination rule. For all y_2, y_2 is not a doctor can be inferred via the universal biconditional elimination rule.