let a, b, c, x, y, z be Complex; <*a,b,c*> (#) <*x,y,z*> = <*(a * x),(b * y),(c * z)*>
<*a,b,c*> (#) <*x,y,z*> =
(<*a,b*> (#) <*x,y*>) ^ <*(c * z)*>
by FMA
.=
<*(a * x),(b * y)*> ^ <*(c * z)*>
by AM2
;
hence
<*a,b,c*> (#) <*x,y,z*> = <*(a * x),(b * y),(c * z)*>
; verum