Rest easy my friend 0Kasushi0
Comparing the AMD 7770 2gb specs. to the AMD 7870 2gb specs. is not going to show a profound difference. A few more cores and such, but nothing that will be like the difference between like "hey.. will this VW Beetle go toe to toe with this Chevy Camero Z28?"
You meet all the other specs. that put you well into the recommended settings, with some spare awesomeness to boot. You will be able to rock med. to high settings across the board with little to no issues provided your have your resolution / frame refresh rates in sync. You may very well even be able to play around with some Ultra settings, but be forewarned that if you see any clipping, or lag, it would be best to dial back so as to be able to enjoy yourself without those hassles. The beauty of FrostBite 3 is how well it renders, even on the lower settings.
So, enjoy yourself! You are good to go!