reserve            S for satisfying_CongruenceSymmetry
                         satisfying_CongruenceEquivalenceRelation
                         TarskiGeometryStruct,
         a,b,c,d,e,f for POINT of S;
reserve S for satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_SAS
              TarskiGeometryStruct,
        q,a,b,c,a9,b9,c9,x1,x2 for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
        a,b,c,d for POINT of S;

theorem Satz3p4:
  for S being satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct
  for a,b,c being POINT of S st between a,b,c & between b,a,c holds a = b
  proof
    let S be satisfying_BetweennessIdentity
             satisfying_Pasch
             TarskiGeometryStruct;
    let a,b,c be POINT of S;
    assume between a,b,c & between b,a,c;
    then consider x be POINT of S such that
A1: between b,x,b & between a,x,a by GTARSKI1:def 11;
    x = a & x = b by A1,GTARSKI1:def 10;
    hence thesis;
  end;
