So I'm trying to understand how to derive the central limit theorem but I'm confused about step 3 in Peter Young's Derivation
In step 3, rightmost part of the equation, why are we taking the sum of all $x_i$, then subtracting them by $X$, which is essentially equal to zero. Won't it turn to $\delta(0)$ ? Are we really saying $\delta(1+2+3-6)$