reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;

theorem Th12:
  for X being non empty set, F being BinOp of X st F is
having_a_unity for x being Element of X holds F.(the_unity_wrt F, x) = x & F.(x
  , the_unity_wrt F) = x
proof
  let X be non empty set, F be BinOp of X;
  assume F is having_a_unity;
  then
A1: the_unity_wrt F is_a_unity_wrt F by Th11;
  let x be Element of X;
  thus thesis by A1,BINOP_1:3;
end;
