Can i put a skin on my iPhone 5 with a screen protector already on it?

So i recently bought a red carbon fiber case for my iPhone 5 and it came with a screen protector. I put them both on but the screen protector had some air bubbles that just won't come out and since the case only covers the back and sides of the phone, you can clearly see the bubbles. I decided that i would get a skin that covers the whole phone so none of the air bubbles would show. Is it ok to put skins on top of a screen protector? Any responces would be appreciated

I think so I did it to my phone and it looked fine and all air bubbles were gone. Hope it helps!