reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct,
        a,b,c,d,c9,x,y,z,p,q,q9 for POINT of S;
reserve              S for satisfying_Tarski-model TarskiGeometryStruct,
        a,a9,b,b9,c,c9 for POINT of S;
reserve S                 for non empty satisfying_Tarski-model
                                    TarskiGeometryStruct,
        A,A9              for Subset of S,
        x,y,z,a,b,c,c9,d,u,p,q,q9 for POINT of S;
reserve S                 for non empty
                            satisfying_Lower_Dimension_Axiom
                            satisfying_Tarski-model
                            TarskiGeometryStruct,
        a,b,c,p,q,x,y,z,t for POINT of S;

theorem :: ExtPerp5A:
  for a,b,c,d,p,q being POINT of S holds
    Collinear a,b,p & Collinear a,b,q & p <> q &
      are_orthogonal a,b,c,d implies are_orthogonal p,q,c,d
  proof
    let a,b,c,d,p,q be POINT of S;
    assume that
A1: Collinear a,b,p and
A2: Collinear a,b,q & p <> q & are_orthogonal a,b,c,d;
A3: p in Line (a,b) by A1,LemmaA1;
    q in Line (a,b) by A2,LemmaA1;
    hence thesis by ExtPerp5,A3,A2;
  end;
