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: If David works, then Jessica is a scientist. For all x_9, x_9 will not cook. For all x_9, x_9 is a scientist if and only if x_9 will cook.
For all x_9, if x_9 were a scientist, then x_9 is cooking can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 cooks, then x_9 is a scientist can be inferred via the universal biconditional elimination rule. For all x_9, x_9 is not a scientist can be inferred via the universal biconditional elimination rule.