What you’re talking about is his proof of (a specialised version) of the Taniyama-Shimura-Weil conjecture[1] which had been proven to imply Fermat’s Last Theorem. The technique he used to prove this was adopted by his students to prove the conjecture in full generality so it now known as the modularity theorem. Given its importance to the Langlands programme it may be that when history looks back on this it will consider this a more important contribution than the fact that it proved FLT even though that is obviously the thing that grabs the headlines, but there’s nothing at all wrong with proving something that implies your goal rather than proving the goal directly. There’s a reason the words “it suffices to show” often turn up in proofs.

[1] https://mathworld.wolfram.com/Taniyama-ShimuraConjecture.htm...