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, if y writes a letter, then y is a musician. For all y, y will play a game if and only if y is a musician. There is at least one y for which y will write a letter if and only if y will play a game.
For all y, if y plays a game, then y is a musician can be inferred via the universal biconditional elimination rule. There is at least one y for which if y writes a letter, then y is playing a game can be inferred via the existential biconditional elimination rule. For all y, if y were a musician, then y is playing a game can be inferred via the universal biconditional elimination rule. There is at least one y for which if y plays a game, then y is writing a letter can be inferred via the existential biconditional elimination rule.