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 z, if z listens to a song, then z is a politician. For all z, z will listen to a song if and only if z will make tea. For all z, z will not make tea. There is at least one z for which if z were a politician, then z is listening to a song.
There is at least one z for which z is a politician if and only if z will listen to a song can be inferred via the existential biconditional introduction rule. There is at least one z for which z will listen to a song if and only if z is a politician can be inferred via the existential biconditional introduction rule. For all z, if z listens to a song, then z is making tea can be inferred via the universal biconditional elimination rule. For all z, if z makes tea, then z is listening to a song can be inferred via the universal biconditional elimination rule. For all z, z will not listen to a song can be inferred via the universal biconditional elimination rule.