Were my previous prayers valid despite adding "and I bear witness that Muhammad is His servant and Messenger" in the the tashahhud?

The minimum sufficient wording for the Tashahhud is: "All greetings are for Allah, peace be upon you, O Prophet, and the mercy of Allah, peace be upon us and upon the righteous servants of Allah. I bear witness that there is no god but Allah, and that Muhammad is the Messenger of Allah," or "that Muhammad is His servant and Messenger."