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 reads a book, then z is happy. For all z, z will read a book if and only if z is a bartender. For all z, if z were happy, then z is a bartender.
For all z, if z reads a book, then z is a bartender can be inferred via the universal transitivity rule. For all z, if z reads a book, then z is a bartender can be inferred via the universal biconditional elimination rule. For all z, if z were a bartender, then z is reading a book can be inferred via the universal biconditional elimination rule.