Ati 4870 with windows 7 and directx11

You'll be fine. Be advised that some games that are marketed as "DX11" really are not. Two examples are:

1. Residential Evil 5 - This games look exactly the same in DX9 mode as it does in DX11 mode. What's the differences? In DX11 mode you will see a drop in performance because the game will switch to the more demanding coding of DX11. The developer openly admitted at the game really only uses DX9 graphics with DX11 coding and no additional DX11 effects.

2. Devil May Cry 4 - Same as above based on screenshots. However, the developer has remained silent on the issue neither confirm or deny that only DX11 coding was used in the game.
 

Who is saying those games are DX11? DMC4 came out in 2008 even... was there a patch or something?