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: There is at least one z for which if z drinks water, then z is writing a letter. For all z, z is rich if and only if z will drink water. For all z, if z writes a letter, then z is rich.
There is at least one z for which if z drinks water, then z is rich can be inferred via the existential transitivity rule. For all z, if z were rich, then z is drinking water can be inferred via the universal biconditional elimination rule. For all z, if z drinks water, then z is rich can be inferred via the universal biconditional elimination rule.