The powerset of $X$ is the set $\mathcal{P}\webleft (X\webright )$ defined by
\[ \mathcal{P}\webleft (X\webright ) \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ U\in P\ \middle |\ U\subset X\webright\} , \]
where $P$ is the set in the axiom of powerset, 
of .
