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Step * 3 1 of Lemma dual-plane_wf


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))
BY
{ (InstLemma `pgeo-triangle-axiom1-dual` [⌜pg⌝]⋅ THEN Auto) }

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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{}  \mforall{}p,q,r:Line.  \mforall{}s:p  \mneq{}  q.  \mforall{}s1:q  \mneq{}  r.    (pgeo-plsep(pg;  p  \mwedge{}  q;  r)  {}\mRightarrow{}  pgeo-plsep(pg;  q  \mwedge{}  r;  p))


By

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Latex:
(InstLemma  `pgeo-triangle-axiom1-dual`  [\mkleeneopen{}pg\mkleeneclose{}]\mcdot{}  THEN  Auto)

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