P[P[P($\Phi$)]] contains 4 elememts.
Now, #non-empty subsets
= $\binom{4}{1}+\binom{4}{2}+\binom{4}{3}$
= 2^{4} - $\binom{4}{0} - \binom{4}{4}$
= 14
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Gatecse
It is quite unfortunate. Never before ...