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_1, if z_1 were a carpenter, then z_1 is writing a letter. For all z_1, if z_1 writes a letter, then z_1 is a carpenter. For all z_1, if z_1 were a bartender, then z_1 is writing a letter.
For all z_1, if z_1 were a bartender, then z_1 is a carpenter can be inferred via the universal transitivity rule. For all z_1, z_1 is a carpenter if and only if z_1 will write a letter can be inferred via the universal biconditional introduction rule. For all z_1, z_1 will write a letter if and only if z_1 is a carpenter can be inferred via the universal biconditional introduction rule.