Was Fermat's last theorem proved based on Peano's postulates?

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Is the proof of Fermat's last theorem solely based on the Peano's postulates $+$ first order logic? Or it contains other axiomatic systems as well? What does it mean from foundations of math perspective to use several axiomatic systems to prove a conjecture? Do we know these axiomatic systems are consistent with one another? I'm not sure if I am asking it the right way, but I think logicians only prove the consistency of the axioms of one system not two different systems.