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

theorem
  z1 <> 0.F_Complex & z2 <> 0.F_Complex & z1" = z2" implies z1 = z2
proof
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
  assume
A1: z1 <> 0.F_Complex;
  assume
A2: z2 <> 0.F_Complex;
  assume z1" = z2";
  then z19" = z2" by A1,Th5
    .= z29" by A2,Th5;
  hence thesis by XCMPLX_1:201;
end;
