theorem Satz6p18: ::GTARSKI_1:46
  A is_line & a <> b & a in A & b in A implies A = Line(a,b)
  proof
    assume that
A1: A is_line and
A2: a <> b and
A3: a in A and
A4: b in A;
    consider p,q such that
A5: p <> q and
A6: A = Line(p,q) by A1;
    consider xa be POINT of S such that
A7: a = xa and
A8: Collinear p,q,xa by A3,A6;
    consider xb be POINT of S such that
A9: b = xb and
A10: Collinear p,q,xb by A4,A6;
    a on_line p,q & b on_line p,q by A5,A7,A8,A9,A10;
    hence thesis by A2,A6,Thequiv2,GTARSKI1:46;
  end;
