- By hypothesis, let $g,h$ be straight lines and let $A$ be the only point that lies on both of them.
- By 3rd axiom of connection, there are at least two points on $g$ and at least two points on $h$. Let $B$ be an additional point on $g$ and $C$ be an additional point on $h.$
- Let $\alpha$ be a plane, in which both, $g$ is located (i.e., by 6th axiom of connection, $A, B$ lie on $\alpha$) and $h$ is located (i.e., by 6th axiom of connection, $A, C$ lie on $\alpha$).
- By construction, $A, B, C$ lie on $\alpha.$
- BY 5th axiom of connection, the points $A, B, C$ completely determine $\alpha.$
- Therefore, there is exactly one plane $\alpha$ such that both straight lines $g$, $h$ are in that plane.

q.e.d

| | | | created: 2019-12-26 13:03:47 | modified: 2019-12-26 13:09:32 | by: *bookofproofs* | references: [8324]

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