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 x_10 for which x_10 will climb a mountain if and only if x_10 is a scientist. For all x_10, if x_10 were fast, then x_10 is climbing a mountain. For all x_10, if x_10 climbs a mountain, then x_10 is fast.
For all x_10, x_10 is fast if and only if x_10 will climb a mountain can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will climb a mountain if and only if x_10 is fast can be inferred via the universal biconditional introduction rule. There is at least one x_10 for which if x_10 climbs a mountain, then x_10 is a scientist can be inferred via the existential biconditional elimination rule. There is at least one x_10 for which if x_10 were a scientist, then x_10 is climbing a mountain can be inferred via the existential biconditional elimination rule.