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: There is at least one y for which y will listen to a song if and only if y will cook. For all y, y will cook if and only if y is excited. For all y, y is excited or y will listen to a song.
For all y, if y cooks, then y is excited can be inferred via the universal 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. For all y, if y were excited, then y is cooking can be inferred via the universal biconditional elimination rule. 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.