Suppose I have the following data.table

dx <- data.table(x=c(1,2,3),tet=list(c(1,2,3),c(4,5),c(3)))

   x   tet
1: 1 1,2,3
2: 2   4,5
3: 3     3

I wanna create a variable test that checks wether each elements of x is in its corresponding set in tet.

I woud like to get

   x   tet  test
1: 1 1,2,3  TRUE
2: 2   4,5 FALSE
3: 3     3  TRUE

I have tried

dx[, test:= x %in% tet]

   x   tet  test
1: 1 1,2,3 FALSE
2: 2   4,5 FALSE
3: 3     3  TRUE

But of course the first row fails because it is comparing 1 against c(1,2,3) and the second row gives me a a false FALSE.

I have also tried using lapply and unlisting but to no avail.

Any ideas?