Deleting all occurrences of element in a nested li

Question

I am trying to delete a specific element from a nested list.

delete(X,L,L1) to delete all occurrences of X from a list L producing the list L1. For exmaple:

?- delete(a,[a,b,[a,d],c],L1). will give us 
[b,[d],c].

I am able to remove the element from a simple non nested list but can't figure out how to remove it in the inner list.

My code:

deletelist(Xs,[],Xs).

deletelist(Xs,[Y|Ys],Zs):- delete(Xs,Y,As),
deletelist(As,Ys,Zs).

Any help would be greatly appreciated