let S be satisfying_CongruenceEquivalenceRelation satisfying_SegmentConstruction TarskiGeometryStruct ; :: thesis: for a, b being POINT of S holds a,b equiv a,b
let a, b be POINT of S; :: thesis: a,b equiv a,b
ex c being POINT of S st
( between a,a,c & a,c equiv a,b ) by GTARSKI1:def 8;
hence a,b equiv a,b by GTARSKI1:def 6; :: thesis: verum