### Nuprl Lemma : eu-be-neq

`∀e:EuclideanPlane. ∀a,b,c:Point.  ((¬(a = b ∈ Point)) `` a_b_c `` (¬(a = c ∈ Point)))`

Proof

Definitions occuring in Statement :  euclidean-plane: `EuclideanPlane` eu-between-eq: `a_b_c` eu-point: `Point` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` not: `¬A` false: `False` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` euclidean-plane: `EuclideanPlane` uimplies: `b supposing a`
Lemmas referenced :  eu-between-eq_wf eu-between-eq-same equal_wf eu-point_wf not_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin equalitySymmetry hypothesis hyp_replacement Error :applyLambdaEquality,  introduction extract_by_obid sqequalHypSubstitution isectElimination setElimination rename because_Cache hypothesisEquality sqequalRule independent_isectElimination independent_functionElimination voidElimination

Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    ((\mneg{}(a  =  b))  {}\mRightarrow{}  a\_b\_c  {}\mRightarrow{}  (\mneg{}(a  =  c)))

Date html generated: 2016_10_26-AM-07_44_43
Last ObjectModification: 2016_07_12-AM-08_11_16

Theory : euclidean!geometry

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