Is the change in flux being equal to negative emf an experimental law? The Wikipedia derivation of emf as a negative change in magnetic flux in time: https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction#cite_note-Krey-25 uses the Maxwell-Faraday equation to derive the transformer emf side of the emf equation, but Wikipedia and other sources I have found use the fact that the change in magnetic flux in time is equal to negative emf to derive the Maxwell-Faraday equation. Is there any way to derive the Maxwell-Faraday equation without the change in flux and emf relationship or the complete emf relationship without the Maxwell-Faraday equation? I understand that Faraday came up with Faraday's Law through experiment but can it be derived using special relativity?
Maxwell's equations, including Faraday's law, along with the Lorentz force law are generally considered to be the fundamental axioms of classical electrodynamics. In this standard framework, the change in flux being the negative of the emf is a consequence of Faraday's law.
For clarity's sake, this is not to say that Maxwell's equations historically precede our rule in question, nor do I mean that Maxwell's equations were not---perhaps somewhat indirectly---discovered experimentally.