reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem Th9:
  --{f} = {-f}
proof
  let i;
  hereby
    assume i in --{f};
    then consider w such that
A1: i = -w and
A2: w in {f};
    w = f by A2,TARSKI:def 1;
    hence i in {-f} by A1,TARSKI:def 1;
  end;
  assume i in {-f};
  then
A3: i = -f by TARSKI:def 1;
  f in ExtREAL & f in {f} by TARSKI:def 1,XXREAL_0:def 1;
  hence thesis by A3;
end;
