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 lawyer. For all x_13, if x_13 were a nurse, then x_13 is listening to a song. For all x_13, if x_13 listens to a song, then x_13 is a poet. For all x_13, if x_13 were a cashier, then x_13 is a nurse. For all x_13, x_13 is a lawyer if and only if x_13 will listen to a song.
For all x_13, if x_13 were a nurse, then x_13 is a poet can be inferred via the universal transitivity rule. For all x_13, if x_13 were a cashier, then x_13 is listening to a song can be inferred via the universal transitivity rule. For all x_13, if x_13 were a lawyer, then x_13 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 listens to a song, then x_13 is a lawyer can be inferred via the universal biconditional elimination rule.