Unordered pair

Set

context $ X,Y$ … set
definiendum $ x\in \{X,Y\} $
postulate $ x = X \lor x = Y $

$\{X,Y\} \equiv \{x \mid x = X \lor x = Y\}$

Discussion

$\{X,X\} = \{x \mid x = X \lor x = X\} = \{x \mid x = X\} = \{X\}$

Reference

Wikipedia: Axiom of pairing

Context

Sets