ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4320 on D4316: Set of singletons
Set of singletons is subset of power set
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathcal{P}(X)$ is the D80: Power set of $X$
(ii) \begin{equation} \mathcal{X} : = \{ \{ x \} : x \in X \} \end{equation}
Then \begin{equation} \mathcal{X} \subseteq \mathcal{P}(X) \end{equation}