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Step * 3 of Lemma dual-plane_wf


1. pg : ProjectivePlaneStructureComplete
2. BasicProjectiveGeometryAxioms(pg)
3. triangle-axiom1(pg)
4. triangle-axiom2(pg)
5. BasicProjectiveGeometryAxioms(dual-plane(pg))
⊢ triangle-axiom1(dual-plane(pg))
BY
{ (Unfold `triangle-axiom1` 0 THEN UnfoldpGeoAbbreviations 0 THEN FoldpGeoAbbreviations 0) }

1
1. pg : ProjectivePlaneStructureComplete
2. BasicProjectiveGeometryAxioms(pg)
3. triangle-axiom1(pg)
4. triangle-axiom2(pg)
5. BasicProjectiveGeometryAxioms(dual-plane(pg))
⊢ ∀p,q,r:Line. ∀s:p ≠ q. ∀s1:q ≠ r.  (pgeo-plsep(pg; p ∧ q; r) ⇒ pgeo-plsep(pg; q ∧ r; p))

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Latex:

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Latex:

1.  pg  :  ProjectivePlaneStructureComplete
2.  BasicProjectiveGeometryAxioms(pg)
3.  triangle-axiom1(pg)
4.  triangle-axiom2(pg)
5.  BasicProjectiveGeometryAxioms(dual-plane(pg))
\mvdash{}  triangle-axiom1(dual-plane(pg))


By

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Latex:
(Unfold  `triangle-axiom1`  0  THEN  UnfoldpGeoAbbreviations  0  THEN  FoldpGeoAbbreviations  0)

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