Consider the following premises. For all x, if x plays squash, then x is climbing a mountain. For all x, if x climbs a mountain, then x is happy. For all x, if x were happy, then x is playing squash. Can we infer the following from them? For all x, x will climb a mountain if and only if x is happy.
 From the fact that for all x, if x were happy, then x is playing squash, and that for all x, if x plays squash, then x is climbing a mountain we can infer that for all x, if x were happy, then x is climbing a mountain. Finally, from the fact that for all x, if x climbs a mountain, then x is happy, and that for all x, if x were happy, then x is climbing a mountain we can infer that for all x, x will climb a mountain if and only if x is happy. Therefore, the answer is yes.