reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;

theorem Th3:
  for R being add-associative right_zeroed right_complementable
  non empty addLoopStr, x being Element of R holds x=0.R iff -x=0.R
proof
  let R be add-associative right_zeroed right_complementable non empty
  addLoopStr, x be Element of R;
  thus x=0.R implies -x=0.R by RLVECT_1:12;
  assume -x = 0.R;
  then -(-x) = 0.R by RLVECT_1:12;
  hence thesis by RLVECT_1:17;
end;
