His mercy isn't a one-time deal. He isn't saving us now, just so He can destroy us later. Once He decided to save us, He commited to saving us every time. Each and every time HaShem redeems us from those who wish to destroy us, it is founded on His redeeming us from Egypt.
This is the meaning of "So that you will tell your children.." (למען תספר באזני בנך) [That HaShem will redeem them from their hardship as well.]
It seems to me, that this is a great foundation for our emunah. He redeemed us from Egypt, so He will redeem us from every hardship. I wonder what the relationship between this idea is and the moment when HaShem first told Avraham of the galut in mitzrayim, and his reaction to that. [He took it as a kindness from HaShem] Perhaps he understood this idea, that HaShem's promise to redeem them from Egypt was a promise to redeem his children for all time, from whichever egypt may oppress them.