EA's System Requirements for the Frostbite 2.5 engine. (Basically for BF3)
Minimum requirements for Battlefield 3
OS: Windows Vista or Windows 7
Processor: Core 2 Duo 2.4 GHz or Althon X2 2.7 GHz
RAM: 2GB
Graphic card: DirectX 10 or 11 compatible Nvidia or AMD ATI card, ATI Radeon 3870 or higher, Nvidia GeForce 8800 GT or higher.
Graphics card memory: 512 MB
Sound card: DirectX compatibl sound card
Hard drive: 15 GB for disc version or 10 GB for digital version
Recommended system requirements for Battlefield 3
OS: Windows 7 64-bit
Processor: Quad-core Intel or AMD CPU
RAM: 4GB
Graphics card: DirectX 11 Nvidia or AMD ATI card, Nvidia GeForce GTX 560 or ATI Radeon 6950.
Graphics card memory: 1 GB
Sound card: DirectX compatibl sound card
Hard drive: 15 GB for disc version or 10 GB for digital version
Your current specification you provided will be able to run Battlefield 3 very optimally with any settings you set it to.
Your System
__________
CPU: AMD Fx-6300 six core black edition 3.5GHz ,Turbo to 4.0GHz
GPU: Sapphire HD 7770 GHz Edition 1GB GDDR5
PSU: 420 Watts
RAM: 4GB DDDR3
__________
Now, your graphics card should not have any issues running at minimal and recommended performance.
The CPU will not bottleneck in any way so you will not have any issues with performance loss.
You have plenty of RAM to spare since most applications will never go over 4 unless you are rendering or recording.
In conclusion, you can and will be able to run at med-high settings with plenty of FPS to spare.