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

theorem
  z1 <> 0.F_Complex & z2 <> 0.F_Complex implies (z1 * z2)" = z1" * z2"
proof
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
  assume
A1: z1 <> 0.F_Complex;
  then
A2: z1" = z19" by Th5;
  assume
A3: z2 <> 0.F_Complex;
  then
A4: z2" = z29" by Th5;
  z1 * z2 <> 0.F_Complex by A1,A3,VECTSP_1:12;
  hence (z1 * z2)" = (z19 * z29)" by Th5
    .= z1" * z2" by A2,A4,XCMPLX_1:204;
end;
