Q: SBB drive dead?

Hi, my Mid 2011 Macbook Air froze this morning. I pressed the power button but after restart I got a blinking question mark. Turns out this happens if the System folder cannot be found.

I tried Recovery Mode but the hard disk is completely gone. I still have the Recovery Disk (which is 8GB), but I guess that’s a physically different drive?

So, can I safely assume the SSD drive is at fault? And if I replace it with a new one, everything will work again? I have an external USB-drive with Yosemite, and when I boot from it, everything works fine. So, is this a good indication that the laptop is fine, or is it still possible the motherboard has hardware issues as well?

thanks!