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, if x were an astronaut, then x is a server. For all x, if x were a server, then x is an astronaut. There is at least one x for which x will climb a mountain if and only if x is an astronaut.
For all x, x is an astronaut if and only if x is a server can be inferred via the universal biconditional introduction rule. For all x, x is a server if and only if x is an astronaut can be inferred via the universal biconditional introduction rule. There is at least one x for which if x climbs a mountain, then x is an astronaut can be inferred via the existential biconditional elimination rule. There is at least one x for which if x were an astronaut, then x is climbing a mountain can be inferred via the existential biconditional elimination rule.