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 z_2 for which if z_2 climbs a mountain, then z_2 is a carpenter. For all z_2, z_2 will climb a mountain. For all z_2, if z_2 were a carpenter, then z_2 is climbing a mountain.
There is at least one z_2 for which z_2 is a carpenter can be inferred via the existential modus ponens rule. There is at least one z_2 for which z_2 will climb a mountain if and only if z_2 is a carpenter can be inferred via the existential biconditional introduction rule. There is at least one z_2 for which z_2 is a carpenter if and only if z_2 will climb a mountain can be inferred via the existential biconditional introduction rule.