reserve A,B,C for Ordinal,
        o for object,
        x,y,z,t,r,l for Surreal,
        X,Y for set;

theorem Th21:
  {-x} = --{x}
proof
  o in {-x} implies o in --{x}
  proof
  assume o in {-x};
    then o =-x & x in {x} by TARSKI:def 1;
    hence thesis by Def4;
  end;
  hence {-x} c= --{x} by TARSKI:def 3;
  let xy be object;
  assume xy in --{x};
  then consider y such that
   A1: y in {x} & xy = -y by Def4;
  x=y by A1,TARSKI:def 1;
  hence thesis by A1,TARSKI:def 1;
end;
