Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:expressedIn |
gptkb:First-order_logic
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of pairing
|
| gptkbp:implies |
Existence of unordered pairs
Existence of singleton sets |
| gptkbp:introducedIn |
gptkb:Zermelo_set_theory
|
| gptkbp:partOf |
gptkb:Zermelo–Fraenkel_set_theory
|
| gptkbp:relatedTo |
gptkb:Axiom_of_extensionality
gptkb:Axiom_of_union gptkb:Axiom_of_empty_set |
| gptkbp:statedIn |
For any sets A and B, there is a set {A, B} containing exactly A and B as elements.
|
| gptkbp:symbol |
∀A ∀B ∃C ∀D (D ∈ C ↔ (D = A ∨ D = B))
|
| gptkbp:usedIn |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:ZFC_set_theory |
| gptkbp:bfsParent |
gptkb:Menge
|
| gptkbp:bfsLayer |
5
|