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 x, x will climb a mountain if and only if x is a carpenter. For all x, x will climb a mountain if and only if x is a carpenter.
For all x, if x climbs a mountain, then x is a carpenter can be inferred via the universal biconditional elimination rule. For all x, if x climbs a mountain, then x is a carpenter can be inferred via the universal biconditional elimination rule. For all x, if x were a carpenter, then x is climbing a mountain can be inferred via the universal biconditional elimination rule. For all x, if x were a carpenter, then x is climbing a mountain can be inferred via the universal biconditional elimination rule.