Database: Axiom of Extensionality

Axiom 66: Extensionality

For all sets x and y , the equality x = y implies that for all classes \mathcal{Z} , if x \in \mathcal{Z} then y \in \mathcal{Z} .

This database entry builds on the following:

  1. Terminology: Class, membership
  2. Terminology: Axiom
  3. Definition: Implication
  4. Definition: Set, proper class
  5. Definition: Universal quantification
  6. Definition: Bounded universal statement
  7. Definition: Equality, distinctness