Full Idea
The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ.
Gist of Idea
The Comprehension Schema says there is a property only had by things satisfying a condition
Source
Peter Smith (Intro to Gödel's Theorems [2007], 22.3)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.190