Fundamental Law of Universal Class

Theorem

 * $\forall x: x \in U$

where:
 * $U$ denotes the universal class
 * $x$ denotes a set

Proof
From the definition of the universal class:


 * $U = \left\{{x: x = x}\right\}$

From this, it follows immediately that:


 * $\forall x: \left({x \in U \iff x = x}\right)$

from which the fundamental law follows directly, since $x = x$.

Source

 * : $\S 6.8$