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: Thomas is playing tennis if and only if Joseph is reading a book. For all x_8, if x_8 plays tennis, then x_8 is climbing a mountain. Joseph is not reading a book. For all x_8, if x_8 climbs a mountain, then x_8 is playing tennis.
If Thomas plays tennis, then Joseph is reading a book can be inferred via the biconditional elimination rule. If Joseph reads a book, then Thomas is playing tennis can be inferred via the biconditional elimination rule. Thomas is not playing tennis can be inferred via the biconditional elimination rule. For all x_8, x_8 will play tennis if and only if x_8 will climb a mountain can be inferred via the universal biconditional introduction rule. For all x_8, x_8 will climb a mountain if and only if x_8 will play tennis can be inferred via the universal biconditional introduction rule.