ThmDex – An index of mathematical definitions, results, and conjectures.
Result R2395 on D13: Empty set
Subset of empty set is empty
Formulation 0
Let $\emptyset$ be the D13: Empty set.
Let $X$ be a D11: Set such that
(i) $X \subseteq \emptyset$ is a D78: Subset of $\emptyset$
Then \begin{equation} X = \emptyset \end{equation}
Formulation 1
Let $\emptyset$ be the D13: Empty set.
Let $X$ be a D11: Set.
Then \begin{equation} X \subseteq \emptyset \quad \implies \quad X = \emptyset \end{equation}
Formulation 2
Let $\emptyset$ be the D13: Empty set.
Let $X$ be a D11: Set.
Then \begin{equation} X \in \mathcal{P}(\emptyset) \quad \implies \quad X = \emptyset \end{equation}