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Step * 1 of Lemma geo-between_functionality

.....antecedent..... 
1. ∀e:EuclideanPlaneStructure
     (BasicGeometryAxioms(e) ⇒ (∀a1,a2,b1,b2,c1,c2:Point.  (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1_b1_c1 ⇐⇒ a2_b2_c2))))
2. e : EuclideanPlane
⊢ BasicGeometryAxioms(e)
BY
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Latex:

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Latex:
.....antecedent..... 
1.  \mforall{}e:EuclideanPlaneStructure
          (BasicGeometryAxioms(e)
          {}\mRightarrow{}  (\mforall{}a1,a2,b1,b2,c1,c2:Point.    (a1  \mequiv{}  a2  {}\mRightarrow{}  b1  \mequiv{}  b2  {}\mRightarrow{}  c1  \mequiv{}  c2  {}\mRightarrow{}  (a1\_b1\_c1  \mLeftarrow{}{}\mRightarrow{}  a2\_b2\_c2))))
2.  e  :  EuclideanPlane
\mvdash{}  BasicGeometryAxioms(e)


By

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Latex:
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