Hilbert's Foundations: Congruence of Differences of Angles

Consider the diagram.

Let's say angle CAB = angle CBA

Let's also angle CAE = angle DBC

Then we can perform angle subtraction. That is,

angle CAB - angle CAE = angle CBA - angle DBC

So then angle EAB = angle DBA

Basically if we have two pairs of equal angles, then their difference is also equal