
theorem Th15:
  for V being RealLinearSpace, M being non empty Affine Subset of
  V, v being VECTOR of V st v in M holds 0.V in M - {v}
proof
  let V be RealLinearSpace;
  let M be non empty Affine Subset of V;
  let v being VECTOR of V;
A1: v in {v} & 0.V = v - v by RLVECT_1:15,TARSKI:def 1;
  assume v in M;
  hence thesis by A1;
end;
