
theorem Th5:
  for x1 be Element of F_Complex for x2 be Complex st x1 =
  x2 & x1 <> 0.F_Complex holds x1" = x2"
proof
  let x1 be Element of F_Complex;
  let x2 be Complex;
  reconsider x4 = x2 as Element of COMPLEX by XCMPLX_0:def 2;
  x4" in COMPLEX by XCMPLX_0:def 2;
  then reconsider x9= x4" as Element of F_Complex by Def1;
  assume that
A1: x1 = x2 and
A2: x1 <> 0.F_Complex;
  0c = 0.F_Complex by Def1;
  then x1 * x9 = 1.F_Complex by A1,A2,Lm2,XCMPLX_0:def 7;
  hence thesis by A2,VECTSP_1:def 10;
end;
