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, x_9 will write a letter or x_9 is not excited. For all x_9, x_9 is excited if and only if x_9 will write a letter.
For all x_9, if x_9 were excited, then x_9 is writing a letter can be inferred via the universal rewriting rule. For all x_9, if x_9 were excited, then x_9 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 writes a letter, then x_9 is excited can be inferred via the universal biconditional elimination rule.