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 is a lawyer if and only if x will climb a mountain. There is at least one x for which x will climb a mountain if and only if x will take a plane. For all x, if x takes a plane, then x is a lawyer.
For all x, if x were a lawyer, then x is climbing a mountain can be inferred via the universal biconditional elimination rule. There is at least one x for which if x climbs a mountain, then x is taking a plane can be inferred via the existential biconditional elimination rule. For all x, if x climbs a mountain, then x is a lawyer can be inferred via the universal biconditional elimination rule. There is at least one x for which if x takes a plane, then x is climbing a mountain can be inferred via the existential biconditional elimination rule.