Database: Axiom of Pairing

Axiom 67: Pairing

For all sets x and y there exists a set T such that for all sets z we have z \in T if and only if we have at least one of the equalities z = x or z = y .

This database entry builds on the following:

  1. Terminology: Axiom
  2. Definition: Bounded existence statement
  3. Definition: Disjunction
  4. Definition: Equivalence
  5. Definition: Set, proper class
  6. Definition: Bounded universal statement
  7. Definition: Equality, distinctness