Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$? If a mathematician would/does make use of Fermat's last theorem in a proof in a publication, would s/he still make use of some kind of caveat, like: "assuming Fermat's last theorem is true" or "assuming the proof is correct", or would it be considered totally unnecessary to even explicitly mention that the theorem is used?
I assume that the theorem is beyond (reasonable?) doubt, but is it so much beyond doubt that it can be used for anything else as well? (E.g., has the proof been checked by a computer? If such a thing is possible.)
(Is there even such a thing as a degree of belief in a proof? Perhaps based on length and complexity? Or is it really a binary thing?)

Let me answer the following (tangential) question.

Is there even such a thing as a degree of belief in a proof?

There is such a thing as degree of belief in a theorem. For example, suppose $T$ is a sentence in the language of set theory expressing a principle of arithmetic. Then if a computer verifies that there is a proof of $T$ from the axioms of $\mathrm{ZFC}$, we can say: "We are $\mathrm{ZFC}$-confident in $T$." Meaning that if $\mathrm{ZFC}$ is sound with respect to arithmetic, then $T$ must actually be true.
The problem, of course, is that present-day mathematics isn't actually formalized and proved from explicitly given axioms. So we cannot (currently) make such statements about, say, Fermat's Last Theorem.
