ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Superset
Definition D955
Proper superset
Formulation 0
Let $E$ be a D11: Set.
A D11: Set $X$ is a proper superset of $E$ if and only if
(1) $\forall \, x \in E : x \in X$ (D954: Superset)
(2) $E \neq X$