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, y is sad or y is not an astronaut. For all y, if y were sad, then y is an astronaut. For all y, if y were an astronaut, then y is sad.
For all y, if y were an astronaut, then y is sad can be inferred via the universal rewriting rule. For all y, y is sad if and only if y is an astronaut can be inferred via the universal biconditional introduction rule. For all y, y is an astronaut if and only if y is sad can be inferred via the universal biconditional introduction rule.