Ordinal equals its Initial Segment/Proof 4

Proof
Let $\alpha$ be an ordinal by Definition 4.

From Strict Ordering of Ordinals is Equivalent to Membership Relation:
 * $\forall \alpha, \beta \in \On: \beta < \alpha \iff \alpha \in \beta$

Hence the statement of the result is equivalent to:
 * $\alpha = \set {\beta \in \On: \beta \in \alpha}$

which is trivially true by definition of a set.