The axiom of Zermelo-Fraenkel set theory which asserts that sets formed by the same elements are equal,
 |
Note that some texts (e.g., Devlin 1993), use a bidirectional equivalent 
preceding "
," while others (e.g., Enderton 1977, Itô 1986),
use the one-way implies 
. However, one-way implication suffices.
Using the notation 
(
is a subset of 
) for 
, the axiom can be written concisely as
 |
where 
denotes logical AND.
