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_7, if x_7 plays a game, then x_7 is writing a letter. For all x_7, x_7 will climb a mountain or x_7 will play a game. For all x_7, x_7 will cook. For all x_7, x_7 will climb a mountain if and only if x_7 will write a letter.
For all x_7, if x_7 climbs a mountain, then x_7 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_7, if x_7 writes a letter, then x_7 is climbing a mountain can be inferred via the universal biconditional elimination rule.