If the beam is in equilibrium, then any and all portions of the beam must be in equilibrium.

We will examine a small portion of the beam element. This portion of the beam must satisfy equilibrium of forces in the horizontal (x) direction.
If the beam is in equilibrium, then any and all portions of the beam must be in equilibrium.
We will examine a small portion of the beam element. This portion of the beam must satisfy equilibrium of forces in the horizontal (x) direction.