theorem Th19:
  --{a} = {-a}
proof
  let z;
  hereby
    assume z in --{a};
    then consider c such that
A1: z = -c and
A2: c in {a};
    c = a by A2,TARSKI:def 1;
    hence z in {-a} by A1,TARSKI:def 1;
  end;
  assume z in {-a};
  then
A3: z = -a by TARSKI:def 1;
  a in COMPLEX & a in {a} by TARSKI:def 1,XCMPLX_0:def 2;
  hence thesis by A3;
end;
