Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb:set_theory |
| gptkbp:category |
gptkb:logic
gptkb:set_theory |
| gptkbp:form |
For any sets A and B, there exists a set C such that for any set D, D is an element of C if and only if D = A or D = B.
|
| https://www.w3.org/2000/01/rdf-schema#label |
axiom of pairing
|
| gptkbp:implies |
the existence of unordered pairs
|
| gptkbp:purpose |
ensures the existence of a set containing exactly two given sets
|
| gptkbp:relatedTo |
gptkb:axiom_of_empty_set
gptkb:axiom_of_extensionality gptkb:axiom_of_union |
| gptkbp:statedIn |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Zermelo_set_theory |
| gptkbp:symbol |
∀A ∀B ∃C ∀D (D ∈ C ↔ (D = A ∨ D = B))
|
| gptkbp:usedIn |
construction of functions
construction of ordered pairs construction of relations |
| gptkbp:bfsParent |
gptkb:Zermelo–Fraenkel_axioms
|
| gptkbp:bfsLayer |
6
|