That’s like saying I need to prove that water is wet.
Natural born....is self-defined and it’s also supported by historical precedent of Fremont being supported as the Republican nominee many years ago.
A historical precedent is just something that happens, and a 'historical precedent' is not a legal one.
Nor does a 'nomination' have anything to do with it since the question of Constitutional qualification is supplied via affidavit by the parties, but the affidavits aren't certified until AFTER the election and at the meeting of the Electoral College.
Basically, Fremont started the race really well, but since he never crossed the finish line your conclusion his situation has any bearing on the Original definition of natural-born is flawed.
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Posts including Supreme Court decisions as well as Congressional Records documenting the FACT that the definition of natural born required citizenship of the parents have been sourced for your convenience.
You may continue to declare yourself the sole arbitrator of the truth, but the FACT is you have yet to provide any substantiation for your assertions.