Altitude of North Celestial Pole equals Latitude of Observer

Theorem
Let $O$ be an observer of the celestial sphere.

Let $P$ be the position of the north celestial pole with respect to $O$.

Let $a$ denote the altitude of $P$.

Let $\phi$ denote the (terrestrial) latitude of $O$.

Then:
 * $a = \phi$

Proof
Let $z$ denote the zenith distance of $P$.

Let $\psi$ denote the (terrestrial) colatitude of $O$.

By definition we have:
 * $a = 90 \degrees - z$
 * $\phi - 90 \degrees - \psi$

Then:

Hence the result.