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_8, x_8 is rich or x_8 will not cook. There is at least one x_8 for which x_8 will write a letter if and only if x_8 is rich. For all x_8, x_8 will write a letter or x_8 will cook.
For all x_8, if x_8 cooks, then x_8 is rich can be inferred via the universal rewriting rule. There is at least one x_8 for which if x_8 writes a letter, then x_8 is rich can be inferred via the existential biconditional elimination rule. There is at least one x_8 for which if x_8 were rich, then x_8 is writing a letter can be inferred via the existential biconditional elimination rule.