Statements (19)
| 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
|
| 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:Zermelo–Fraenkel_set_theory
gptkb:Set_Theory |
| gptkbp:bfsLayer |
5
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Pairing
|