reserve z,z1,z2,z3,z4 for Element of F_Complex;

theorem
  z <> 0.F_Complex implies (-z)" = -(z")
proof
  reconsider z1=z as Element of COMPLEX by Def1;
A1: -z = -z1 by Th2;
  assume
A2: z <> 0.F_Complex;
  then
A3: z1" = z" by Th5;
  -z <> 0.F_Complex by A2,VECTSP_1:28;
  hence (-z)" = (-z1)" by A1,Th5
    .= -(z1") by XCMPLX_1:222
    .= -(z") by A3,Th2;
end;
