How to negate %in%

I can subset a "SpatialPolygonsDataFrame" from a
data frame containing a smaller subset of IDs. For
example below.

smaller_sp <- large_sp [large_sp$ID %in% smaller_df$ID,]

Given the above how can I do the logically opposite from
the %in% operation and get all those IDs not %in%?

I am processing two different sets of polygons (A,B) in
a loop. Operation is seeing in center points in polys B
fall in A. I would like to remove the spatial polygons
that I found (B) as I traverse the geographical area.

Thanks,
Jim Burke