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WDUnordered pair

Definition·D003

The pair {a, b} contains exactly a and b.

The singleton is .
In words
An object x belongs to the pair of a and b exactly when x equals a or x equals b.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 · A09 (computed from the citation graph, not asserted).

Remarks

The unordered pair; its existence for any is guaranteed by Pairing. The singleton is the special case . In Lean and Mathlib the pair is built by iterated insertion, whence the leanName Set.insert.
Wikipedia ↗Set.insert ↗

Used by

A02D006D010L01L05L15L24T06T12
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