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_1, if z_1 plays a game, then z_1 is climbing a mountain. There is at least one z_1 for which z_1 will climb a mountain if and only if z_1 will play a game.
There is at least one z_1 for which if z_1 climbs a mountain, then z_1 is playing a game can be inferred via the existential biconditional elimination rule. There is at least one z_1 for which if z_1 plays a game, then z_1 is climbing a mountain can be inferred via the existential biconditional elimination rule.