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_13, x_13 is a bartender if and only if x_13 will drink water. For all x_13, if x_13 drinks water, then x_13 is a bartender. For all x_13, if x_13 writes a letter, then x_13 is making tea. For all x_13, x_13 will not drink water. There is at least one x_13 for which if x_13 makes tea, then x_13 is a bartender.
There is at least one x_13 for which if x_13 writes a letter, then x_13 is a bartender can be inferred via the existential transitivity rule. For all x_13, if x_13 were a bartender, then x_13 is drinking water can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 drinks water, then x_13 is a bartender can be inferred via the universal biconditional elimination rule. For all x_13, x_13 is not a bartender can be inferred via the universal biconditional elimination rule.