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 listens to a song, then y is cooking. There is at least one y for which y will cook if and only if y will listen to a song.
There is at least one y for which if y cooks, then y is listening to a song can be inferred via the existential biconditional elimination rule. There is at least one y for which if y listens to a song, then y is cooking can be inferred via the existential biconditional elimination rule.