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: There is at least one y for which y will not write a letter. For all y, if y were an electrician, then y is listening to a song. For all y, if y writes a letter, then y is listening to a song. For all y, if y listens to a song, then y is writing a letter.
There is at least one y for which y will not listen to a song can be inferred via the existential modus tollens rule. For all y, if y were an electrician, then y is writing a letter can be inferred via the universal transitivity rule. For all y, y will write a letter if and only if y will listen to a song can be inferred via the universal biconditional introduction rule. For all y, y will listen to a song if and only if y will write a letter can be inferred via the universal biconditional introduction rule.