let z1, z2 be Element of F_Complex; :: thesis: ( z1 <> 0. F_Complex & z2 <> 0. F_Complex implies (z1 ") / z2 = (z1 * z2) " )
reconsider z19 = z1, z29 = z2 as Element of COMPLEX by Def1;
assume A1: z1 <> 0. F_Complex ; :: thesis: ( not z2 <> 0. F_Complex or (z1 ") / z2 = (z1 * z2) " )
assume A2: z2 <> 0. F_Complex ; :: thesis: (z1 ") / z2 = (z1 * z2) "
then A3: z1 * z2 <> 0. F_Complex by A1, VECTSP_1:12;
z1 " = z19 " by A1, Th5;
hence (z1 ") / z2 = (z19 ") / z29 by A2, Th6
.= (z19 * z29) " by XCMPLX_1:221
.= (z1 * z2) " by A3, Th5 ;
:: thesis: verum