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Step * of Lemma geo-zero-angle-congruence-subst

∀g:EuclideanPlane. ∀a,b,c,x,y,z:Point.  (abc ≅a xyx ⇒ aba ≅a xyx)
BY
{ (Auto THEN InstLemma `geo-zero-angle-congruence-out` [⌜g⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜x⌝;⌜y⌝]⋅ THEN Auto) }

1
1. g : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. x : Point
6. y : Point
7. z : Point
8. abc ≅a xyx
9. out(b ac)
⊢ aba ≅a xyx

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Latex:

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Latex:
\mforall{}g:EuclideanPlane.  \mforall{}a,b,c,x,y,z:Point.    (abc  \mcong{}\msuba{}  xyx  {}\mRightarrow{}  aba  \mcong{}\msuba{}  xyx)


By

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Latex:
(Auto  THEN  InstLemma  `geo-zero-angle-congruence-out`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THEN  Auto)

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