Statements (17)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
gptkbp:consequence |
Existence of the set of all subsets of a given set
|
https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Power Set
|
gptkbp:implies |
Power set
|
gptkbp:namedAfter |
Power set
|
gptkbp:partOf |
gptkb:Zermelo-Fraenkel_set_theory
|
gptkbp:relatedTo |
gptkb:Axiom_of_Extensionality
gptkb:Axiom_of_Infinity gptkb:Axiom_of_Union |
gptkbp:state |
For any set x, there is a set y such that the elements of y are exactly the subsets of x.
|
gptkbp:statedIn |
gptkb:Zermelo-Fraenkel_set_theory
|
gptkbp:symbol |
∀x ∃y ∀z (z ∈ y ↔ z ⊆ x)
|
gptkbp:usedIn |
gptkb:Mathematics
gptkb:Set_theory |
gptkbp:bfsParent |
gptkb:set_theory
|
gptkbp:bfsLayer |
4
|