electric circuits - Is Ohm's law obeyed in power transmission?

We learnt in high school that according to Ohm's law $V/I=R$. We also learnt that during power transmission in an electric line $P=VI$ and that in order to minimize loss voltage is raised. As a consequence current is reduced. This contradicts with the Ohm's law which states that $V$ is proportional to $I$. What is the difference?

Answer

The usable voltage out of a battery or a generator is $V = E - i R_{wire} $ where $E$ is the rated voltage (being 12V or 768kV), $i$ is the current and $R_{wire}$ is the resistance of the wire. The current is usually found by the load on the circuit as $i=\frac{V}{R_{load}}$.

So alltogether with power $P=i V$ we have

$$ V = \frac{E R_{load}}{R_{load}+R_{wire}} \\ P = \frac{E^2 R_{load}}{(R_{load}+R_{wire})^2} $$

Only when the wire resitance is negligible you get $$V=E \\ P=\frac{V^2}{R_{load}} $$