signal analysis - $lim limits_{a to 0} frac{1}{a}[u(frac{t}{a}+frac{1}{2})-u(frac{t}{a}-frac{1}{2})]= delta(t) $

It would be very helpful if someone could provide the intuitive reasoning and mathematical proof for:

$$F_a(t):=\frac{1}{a}\left[u\left(\frac{t}{a}+\frac{1}{2}\right)-u\left(\frac{t}{a}-\frac{1}{2}\right)\right]$$

$$ \lim_{a \to 0} F_a(t) = \delta(t) $$

where $u(t)$ is the unit step function and $\delta(t)$ is the unit impulse function.