i don't see anything wrong with that.
since is also an automorphism, you can even say that (x + (4))y = 0 for all x,y in I.
Let R be ring, I ideal of R
Let f is automorphism of R.
let say: (f(x)+4 )f(y)=0, x,y I
if i say (f(x)+4 ) y = 0, x,y
whether the statement was valid?
if yes, any reason to explain that? (i know f is invertible cause f is 1-1, but whether there is a more specific explanation?)