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_9, if x_9 plays tennis, then x_9 is writing a letter. There is at least one x_9 for which x_9 is a nurse if and only if x_9 will write a letter. For all x_9, x_9 will play tennis.
For all x_9, x_9 will write a letter can be inferred via the universal modus ponens rule. There is at least one x_9 for which if x_9 were a nurse, then x_9 is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 writes a letter, then x_9 is a nurse can be inferred via the existential biconditional elimination rule.