Statements (18)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
gptkbp:formedBy |
gptkb:Ernst_Zermelo
|
gptkbp:hasWikidataID |
gptkb:Q190611
|
gptkbp:hasWikipediaPage |
https://en.wikipedia.org/wiki/Axiom_of_pairing
|
https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Pairing
|
gptkbp:implies |
Existence of unordered pairs
|
gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
gptkbp:relatedTo |
gptkb:Axiom_of_Empty_Set
gptkb:Axiom_of_Extensionality gptkb:Axiom_of_Union |
gptkbp:sentence |
For any sets A and B, there is a set containing exactly A and B as elements.
|
gptkbp:statedIn |
gptkb:Zermelo–Fraenkel_set_theory
|
gptkbp:symbol |
∀A ∀B ∃C ∀x (x ∈ C ↔ (x = A ∨ x = B))
|
gptkbp:usedIn |
gptkb:Set_theory
Construction of ordered pairs |
gptkbp:bfsParent |
gptkb:set_theory
|
gptkbp:bfsLayer |
4
|