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 work if and only if x_10 is a writer. For all x_10, x_10 is not a nurse. For all x_10, if x_10 were an office clerk, then x_10 is a nurse. For all x_10, x_10 is an office clerk or x_10 will work.
For all x_10, x_10 is not an office clerk can be inferred via the universal modus tollens rule. There is at least one x_10 for which if x_10 works, then x_10 is a writer can be inferred via the existential biconditional elimination rule. There is at least one x_10 for which if x_10 were a writer, then x_10 is working can be inferred via the existential biconditional elimination rule.