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 z, if z works, then z is writing a letter. For all z, if z writes a letter, then z is working. There is at least one z for which z will climb a mountain if and only if z will write a letter.
For all z, z will work if and only if z will write a letter can be inferred via the universal biconditional introduction rule. For all z, z will write a letter if and only if z will work can be inferred via the universal biconditional introduction rule. There is at least one z for which if z climbs a mountain, then z is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one z for which if z writes a letter, then z is climbing a mountain can be inferred via the existential biconditional elimination rule.