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, if x writes a letter, then x is sad. There is at least one x for which x will write a letter if and only if x will play tennis. For all x, x is not sad. For all x, if x plays tennis, then x is writing a letter.
For all x, x will not write a letter can be inferred via the universal modus tollens rule. For all x, if x plays tennis, then x is sad can be inferred via the universal transitivity rule. There is at least one x for which if x writes a letter, then x is playing tennis can be inferred via the existential biconditional elimination rule. There is at least one x for which if x plays tennis, then x is writing a letter can be inferred via the existential biconditional elimination rule.