Recently, I figured out that a college of mine has had published during years a proof of a theorem in which he was actually proving a deeper result which we both thought to be still open. After a closer look to his proof I found that, taking a bit more of care and putting some additional emphasis in certain parts of his previous proof, he was actually proving the other still-thought-to-be-open problem: the construction was absolutely the same and therefore the proof of the previously published theorem was certainly a better argument than we first thought. I am curious now about this phenomenon happening more often. Do you know some other recent (let say from 1700 to our days) examples of this phenomenon of proofs being stronger than initially stated or proving more than thought in the first moment?

Recently, I figured out that a colleague of mine has had published during recent years a proof of a theorem in which he was actually proving a deeper result which we both thought to be still open. After a closer look at his proof I found that, taking a bit more care and putting some additional emphasis in certain parts of his previous proof, he was actually proving the other still-thought-to-be-open problem: the construction was absolutely the same and therefore the proof of the previously published theorem was certainly a better argument than we first thought. I am curious now about this phenomenon happening more often. Do you know some other recent (let's say from 1700 to the current day) examples of this phenomenon of proofs being stronger than initially stated or proving more than thought at first?