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
