Consider the following premises. There is at least one x for which x will climb a mountain if and only if x is a bartender. For all x, if x plays tennis, then x is a bartender. For all x, if x climbs a mountain, then x is playing tennis. Can we infer the following from them? For all x, if is not true that x will climb a mountain if and only if x is a bartender.
 From the fact that there is at least one x for which x will climb a mountain if and only if x is a bartender we can infer that there is at least one x for which if x were a bartender, then x is climbing a mountain. From the fact that for all x, if x climbs a mountain, then x is playing tennis, and that for all x, if x plays tennis, then x is a bartender we can infer that for all x, if x climbs a mountain, then x is a bartender. Finally, from the fact that for all x, if x climbs a mountain, then x is a bartender, and that there is at least one x for which if x were a bartender, then x is climbing a mountain we can infer that there is at least one x for which x will climb a mountain if and only if x is a bartender, which contradicts that For all x, if is not true that x will climb a mountain if and only if x is a bartender. Therefore, the answer is no.