
# 12.8: Axiom h-V


Finally, we need to check that the Axiom h-V holds; that is, we need to prove the following claim.

Theorem $$\PageIndex{1}$$

Claim For any h-line $$\ell$$ and any h-point $$P\notin\ell$$ there are at least two h-lines that pass thru $$P$$ and have no points of intersection with $$\ell$$.

Applying the main observation we can assume that $$P$$ is the center of the absolute.
Exercise $$\PageIndex{1}$$