[6] Use Hilbert's axioms of incidence and betweenness to complete the proof of the following theorem. A picture has been provided for your convenience, but be careful not to rely on it. Theorem: If A and B are any two distinct points, then there exists a point X between A and B. Hypothesis: Points A and B. Conclusion: There exists a point X so that A-X-B. Statements 1) Points A and B 2) There exists a point E not on AB 3) There exists a point F so that A-E-F 4) There exists a point G so that F-B-G 5) EG intersects BF at G, hence cannot intersect at another point 6) EG contains a point X between A and B PROOF 1) Hypothesis 2) 3) 4) 5) 6) Reasons EX B