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 rich or x_13 is excited. For all x_13, x_13 will work if and only if x_13 is excited. For all x_13, if x_13 works, then x_13 is a mechanic. There is at least one x_13 for which if x_13 were rich, then x_13 is working.
There is at least one x_13 for which if x_13 were rich, then x_13 is a mechanic can be inferred via the existential transitivity rule. For all x_13, if x_13 works, then x_13 is excited can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were excited, then x_13 is working can be inferred via the universal biconditional elimination rule.