Full Idea
Empty Set Axiom: ∃x ∀y ¬ (y ∈ x). There is a set x which has no members (no y's). The empty set exists. There is a set with no members, and by extensionality this set is unique.
Gist of Idea
Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 2.3)
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.70
A Reaction
A bit bewildering for novices. It says there is a box with nothing in it, or a pair of curly brackets with nothing between them. It seems to be the key idea in set theory, because it asserts the idea of a set over and above any possible members.