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 nurse or y_1 will not listen to a song. There is at least one y_1 for which y_1 is a nurse if and only if y_1 will listen to a song.
For all y_1, if y_1 listens to a song, then y_1 is a nurse can be inferred via the universal rewriting rule. There is at least one y_1 for which if y_1 were a nurse, then y_1 is listening to a song can be inferred via the existential biconditional elimination rule. There is at least one y_1 for which if y_1 listens to a song, then y_1 is a nurse can be inferred via the existential biconditional elimination rule.