Can I use my 12 word recovery phrase to recover my bitcoin with a different wallet provider?

If blockchain.info was to go down, would I be able to recover the coins into a different wallet with just the 12 word recovery phrase?

I created a blockchain wallet but I can't seem to find any way to export the private keys, and after some research it seems like blockchain has replaced private keys with mnemonic phrases. How would I go about getting my coins into a different wallet with just the mnemonic phrase, if blockchain were to go down?