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I like to keep in mind a simplified (and sometimes imprecise) version of the theorem. For example, consider the Hahn-Banach Theorem. When I think about it the first thing that comes to my mind is

"A linear functional $f$ dominated by $p$ in a subspace can be extended to a linear functional $F$ dominated by $p$ in the whole space."

And then I might may or might not remember the details. I would say the same thing about proofs. I try to keep in mind the main steps and other results the proof relies on.

"A linear functional $f$ dominated by $p$ in a subspace can be extended to a linear functional $F$ dominated by $p$ in the whole space."