let z be Quaternion; :: thesis: ( z = 0 implies z *' = 0 )
assume A1: z = 0 ; :: thesis: z *' = 0
then A2: Rea z = 0 by Lm6, Th16;
A3: Im1 z = 0 by A1, Lm6, Th16;
A4: Im2 z = 0 by A1, Lm6, Th16;
Im3 z = 0 by A1, Lm6, Th16;
hence z *' = 0 by A2, A3, A4, Lm6, Th36; :: thesis: verum