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, if y_2 were an astronaut, then y_2 is not a writer. For all y_2, if y_2 writes a letter, then y_2 is an astronaut. For all y_2, y_2 is a writer. There is at least one y_2 for which if y_2 were an astronaut, then y_2 is writing a letter.
For all y_2, y_2 is not an astronaut can be inferred via the universal modus tollens rule. There is at least one y_2 for which y_2 is an astronaut if and only if y_2 will write a letter can be inferred via the existential biconditional introduction rule. There is at least one y_2 for which y_2 will write a letter if and only if y_2 is an astronaut can be inferred via the existential biconditional introduction rule.