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, x will not take a plane. For all x, x will take a plane if and only if x will listen to a song. John is listening to a song if and only if it is snowing.
If John listens to a song, then it is snowing can be inferred via the biconditional elimination rule. If it snows, then John is listening to a song can be inferred via the biconditional elimination rule. For all x, if x takes a plane, then x is listening to a song can be inferred via the universal biconditional elimination rule. For all x, if x listens to a song, then x is taking a plane can be inferred via the universal biconditional elimination rule. For all x, x will not listen to a song can be inferred via the universal biconditional elimination rule.