# logic – succession in quantifier clause

In first order logic, why do we say that:
$$exists$$ $$xi$$ $$phi$$ is satisfied by succession si iff there is a different succession from s that satisfied $$phi$$?

For instance, maybe the only succession that satisfies $$phi$$ is actually si, and there is no other succession different from si that satisfies $$phi$$. Why there must be a different succession?