- By hypothesis, let $\alpha$ be a plane and $g$ be a straight line that is not in $\alpha.$
- If there is no point $A,$ that lies on both, $g$ and $\alpha$ then there is nothing left to be proven.
- Therefore, let $A$ lie on both, $g$ and $\alpha.$
- Assume, there is another point $B\neq A$ that also lies on both, $g$ and $\alpha.$
- By assumption and 6th axiom of connection, $g$ would be in $\alpha,$ contradicting the hypothesis.
- Therefore, there is at most one point $A,$ that lies on both.

q.e.d

| | | | created: 2019-12-26 12:19:48 | modified: 2019-12-26 12:22:33 | by: *bookofproofs* | references: [8324]

(none)

[8324] **Hilbert, David**: “Grundlagen der Geometrie”, Leipzig, B.G. Teubner, 1903