External Angle of Triangle equals Sum of other Internal Angles/Proof 2

Theorem
The external angle of a triangle equals the sum of the other two internal angles.

Proof
Let $\triangle ABC$ be a triangle.

From Sum of Angles of Triangle Equals Two Right Angles, we have:
 * $(1): \angle ABC + \angle BCA + \angle CAB = 180^\circ$

Extend $AB$ to $D$.

By Two Angles on Straight Line make Two Right Angles, we have:
 * $(2): \angle ABC + \angle CBD = 180^\circ$

Combining $(1)$ and $(2)$ and using Equality is Transitive:
 * $\angle ABC + \angle BCA + \angle CAB = \angle ABC + \angle CBD$

By using commom notion 3:
 * $\angle BCA + \angle CAB = \angle CBD$

By using Equality is Symmetric:
 * $\angle CBD = \angle BCA + \angle CAB$