Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $AB\cap CD=\{E\}$, $AC\cap BD=\{F\}$ and $AD\cap BC=\{G\}$. Then the points $E,F,G$ are not collinear.

I tried to prove by contradiction defining a graph on set $\{A,B,C,D\}$ with edge between two points if they lie on different sides of the line $EFG$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.

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