Sorry. No dice. Your quote wasn’t a quote and the intended article has nothing to do with leaving the union. Here is Article 4 as it is actually written.
“Article IV
Section 1.
Full faith and credit shall be given in each state to the public acts, records, and judicial proceedings of every other state. And the Congress may by general laws prescribe the manner in which such acts, records, and proceedings shall be proved, and the effect thereof. “
The states that attempted secession never gave the congress the opportunity to prescribe the manner in which secession would be proved.