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, if x_13 were a cashier, then x_13 is a mechanic. For all x_13, x_13 will play squash if and only if x_13 is a cashier. For all x_13, if x_13 were a mechanic, then x_13 is a cashier. For all x_13, if x_13 were a mechanic, then x_13 is an astronaut.
For all x_13, if x_13 were a cashier, then x_13 is an astronaut can be inferred via the universal transitivity rule. For all x_13, x_13 is a cashier if and only if x_13 is a mechanic can be inferred via the universal biconditional introduction rule. For all x_13, x_13 is a mechanic if and only if x_13 is a cashier can be inferred via the universal biconditional introduction rule. For all x_13, if x_13 plays squash, then x_13 is a cashier can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a cashier, then x_13 is playing squash can be inferred via the universal biconditional elimination rule.