R combine cell content if condition true

I want to combine the content of two cells if several conditions are true.

I have the follwoing dataframe:

df <- data.frame(page = c("a1","a1","a2","a2","a3"),
                 keyword = c("a,b,c", "a,b,c,d", "d,e,f","g","a"))

The conditions in pseudo code:

if some cells of column page are equal (e.g. a1 and a2 appear two times)
then combine the content of column keyword and delete duplicate content. 

This means in the end I need a dataframe, which looks like this:

page | keyword

a1 | a,b,c,d

a2 | d,e,f,g

a3 | a

I already tried different approaches but didnt receive the correct result. Does anybody has an idea?