The phrase "old axiom" refers to a well-known saying or idea that has been widely accepted and passed down through many generations. It represents a traditional piece of wisdom or common belief. Full definition
There's an age - old axiom in Washington that goes, «Personnel is policy.» (inc.com)
As I get older I'm beginning to re-think old axioms. (madame-ostrich.com)
At its heart, In Good Company is a love song to hoary old axioms concerning love, loyalty, and honour — its charms are old - fashioned and its bromides, if not entirely unexpected, are at least earned. (filmfreakcentral.net)