How can I remove all cells with "NA" value by columns

This question is not a duplicate because my data.frame does not have the same amount of NA values in all Columns and therefore the solution mentioned in that question does not work.

I have a data.frame with a lot of NA values and I would like to delete all cells (important: not rows or columns, cells) that have NA values. The original would look like this:

A  B
1  NA
NA 2
2  NA
NA NA
NA NA
NA 4
3  5

The desired result would look like this:

A  B
1  2
2  4 
3  5

The number of columns would have to stay the same, but it does not matter if the values remain on the same rows. They can just be moved up.

I could image one could delete all cells with the condition NA (maybe with apply) and get the result. Or maybe a simple sorting ?

Thanks.

Update:

A   B   C
1       3
    2   
4       3

    1   2

3       5
        4
    9   
7       1