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_9 for which x_9 is a doctor if and only if x_9 will cook. For all x_9, x_9 will not write a letter. For all x_9, x_9 is a doctor if and only if x_9 will write a letter. For all x_9, if x_9 were a doctor, then x_9 is writing a letter.
For all x_9, x_9 is not a doctor can be inferred via the universal modus tollens rule. For all x_9, if x_9 were a doctor, then x_9 is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 were a doctor, then x_9 is cooking can be inferred via the existential biconditional elimination rule. For all x_9, if x_9 writes a letter, then x_9 is a doctor can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 cooks, then x_9 is a doctor can be inferred via the existential biconditional elimination rule. For all x_9, x_9 is not a doctor can be inferred via the universal biconditional elimination rule.