theorem ThB3:
  -{g} = {-g}
proof
  thus -{g} c= {-g}
  proof
    let x be object;
    assume x in -{g};
    then consider h such that
A1: x = -h and
A2: h in {g};
    h = g by A2,TARSKI:def 1;
    hence thesis by A1,TARSKI:def 1;
  end;
  let x be object;
  assume x in {-g};
  then
A3: x = -g by TARSKI:def 1;
  g in {g} by TARSKI:def 1;
  hence thesis by A3;
end;
