Axioms:
<UL>
   <LI>$P_1$:
    Existence of Parallel
   \[
       \forall r \in \mathcal{R},
       ~~
       \forall P \notin r:
       \exists s:
       r \parallel s
       \wedge
       P \in s
    \]
    </LI>
    <LI>$P_2$:
    Unicity of Parallel
    \[
       \forall r \in \mathcal{R},
       ~~
       \forall P \notin r:
       \exists ! s:
       r \parallel s
       \exists
       P \in s
    \]

      <H4>Humanity trying to prove this for 2000 years...</H4>
   </LI>
</UL>