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 Elisabeth were an office clerk, then David is playing a game. For all x_13, x_13 will play a game if and only if x_13 will take a plane. If David takes a plane, then Patricia is writing a letter.
For all x_13, if x_13 plays a game, then x_13 is taking a plane can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 takes a plane, then x_13 is playing a game can be inferred via the universal biconditional elimination rule.