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, z will climb a mountain if and only if z will take a plane. For all z, z will listen to a song if and only if z will take a plane. For all z, if z listens to a song, then z is climbing a mountain.
For all z, if z climbs a mountain, then z is taking a plane can be inferred via the universal biconditional elimination rule. For all z, if z listens to a song, then z is taking a plane can be inferred via the universal biconditional elimination rule. For all z, if z takes a plane, then z is climbing a mountain can be inferred via the universal biconditional elimination rule. For all z, if z takes a plane, then z is listening to a song can be inferred via the universal biconditional elimination rule.