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: Sarah is excited if and only if Michael is happy. For all x_12, x_12 will write a letter. For all x_12, if x_12 were excited, then x_12 is not writing a letter.
If Sarah were excited, then Michael is happy can be inferred via the biconditional elimination rule. If Michael were happy, then Sarah is excited can be inferred via the biconditional elimination rule. For all x_12, x_12 is not excited can be inferred via the universal modus tollens rule.