By implication? Pray, where does it say by implication?!? What the Constitution says is
'The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
Is the power of secession or directions for leaving the union somewhere in the document I missed? No? Then it falls under the 10th as a power not delegated to the federal government. Look at it this way. I enter into a contract with you, but send you back the contract with certain changes that I deem necessary, and you, by your silence, accept those changes. We for some reason have to go in front of a court. Any court in the land that follows common law is going to side with me on a judgement because you did not voice an objection to the changed agreement.
This is the same situation. New York, Kentucky, and Rhode Island sent back a changed agreement. The Southern states recognized that change, and of course after watching their northern brethren threaten secession time and time again since the inception of the document, decided to themselves secede. It was only in '69 after that infamous politicized decision that secession was declared illegal. Interesting that it took eight years. You would have thought that during the four years of the war that the government of these United States would have brought something to trial to have secession declared illegal. Ah, but Sal fixed that one for them didn't he? Of course to cover his own tail as well
What the Constitution also says, billbears, is that a state can only be admitted to the Union on the majority vote of Congress. States cannot combine without congressional approval or split up without congressional approval or change their borders one fraction of an inch without congressional approval. Obviously the power to determine the status of a state was a power reserved to Congress by the Constitution.