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 y, if y climbs a mountain, then y is happy. For all y, y is happy or y will not climb a mountain. There is at least one y for which if y were happy, then y is climbing a mountain.
For all y, if y climbs a mountain, then y is happy can be inferred via the universal rewriting rule. There is at least one y for which y is happy if and only if y will climb a mountain can be inferred via the existential biconditional introduction rule. There is at least one y for which y will climb a mountain if and only if y is happy can be inferred via the existential biconditional introduction rule.