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_5, x_5 will play tennis if and only if x_5 is a scientist. For all x_5, x_5 is a scientist if and only if x_5 is a bartender. For all x_5, if x_5 were a bartender, then x_5 is excited. For all x_5, x_5 is not excited.
For all x_5, x_5 is not a bartender can be inferred via the universal modus tollens rule. For all x_5, if x_5 plays tennis, then x_5 is a scientist can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were a scientist, then x_5 is a bartender can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were a scientist, then x_5 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were a bartender, then x_5 is a scientist can be inferred via the universal biconditional elimination rule.