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_1, y_1 is a carpenter if and only if y_1 will read a book. There is at least one y_1 for which y_1 will play a game. For all y_1, y_1 is a carpenter.
There is at least one y_1 for which y_1 will play a game and y_1 is a carpenter can be inferred via the existential conjunction rule. Some carpenters will play a game can be inferred via the existential conjunction rule. For all y_1, if y_1 were a carpenter, then y_1 is reading a book can be inferred via the universal biconditional elimination rule. For all y_1, if y_1 reads a book, then y_1 is a carpenter can be inferred via the universal biconditional elimination rule.