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 y_3, if y_3 were rich, then y_3 is playing squash. There is at least one y_3 for which if y_3 were a soldier, then y_3 is a nurse. For all y_3, if y_3 plays squash, then y_3 is sad. For all y_3, if y_3 were sad, then y_3 is a soldier.
For all y_3, if y_3 were rich, then y_3 is sad can be inferred via the universal transitivity rule. For all y_3, if y_3 plays squash, then y_3 is a soldier can be inferred via the universal transitivity rule. There is at least one y_3 for which if y_3 were sad, then y_3 is a nurse can be inferred via the existential transitivity rule.