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: If it rains, then Michael is working. For all y, y will listen to a song if and only if y will work. If Michael listens to a song, then it is raining.
If Michael listens to a song, then Michael is working can be inferred via the transitivity rule. For all y, if y listens to a song, then y is working can be inferred via the universal biconditional elimination rule. For all y, if y works, then y is listening to a song can be inferred via the universal biconditional elimination rule.