### Nuprl Lemma : eu-cong-angle-symm

`∀e:EuclideanPlane. ∀a,b,c:Point.  abc = cba supposing (¬(a = b ∈ Point)) ∧ (¬(c = b ∈ Point))`

Proof

Definitions occuring in Statement :  eu-cong-angle: `abc = xyz` euclidean-plane: `EuclideanPlane` eu-point: `Point` uimplies: `b supposing a` all: `∀x:A. B[x]` not: `¬A` and: `P ∧ Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` and: `P ∧ Q` not: `¬A` implies: `P `` Q` false: `False` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` prop: `ℙ` eu-cong-angle: `abc = xyz` cand: `A c∧ B` uiff: `uiff(P;Q)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` exists: `∃x:A. B[x]`
Lemmas referenced :  eu-three-segment eu-length-flip eu-between-eq-symmetry eu-extend-exists exists_wf eu-congruent_wf eu-between-eq_wf eu-congruent-flip eu-congruent-iff-length euclidean-plane_wf equal_wf not_wf eu-point_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality lambdaEquality dependent_functionElimination hypothesisEquality voidElimination equalityEquality lemma_by_obid isectElimination setElimination rename hypothesis productEquality because_Cache independent_pairFormation independent_functionElimination equalitySymmetry dependent_set_memberEquality independent_isectElimination dependent_pairFormation equalityTransitivity

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    abc  =  cba  supposing  (\mneg{}(a  =  b))  \mwedge{}  (\mneg{}(c  =  b))

Date html generated: 2016_06_16-PM-01_32_01
Last ObjectModification: 2016_05_23-AM-11_11_03

Theory : euclidean!geometry

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