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 were a bartender, then y is a doctor. There is at least one y for which y will drink water if and only if y will listen to a song. For all y, y will drink water or y is a bartender. For all y, if y were a doctor, then y is listening to a song.
For all y, if y were a bartender, then y is listening to a song can be inferred via the universal transitivity rule. There is at least one y for which if y drinks water, 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 drinking water can be inferred via the existential biconditional elimination rule.