Why would the Arkansas Territory be allowed to have slavery after 1820?

Though ostensibly free-soil, the new state had a constitution that permitted indentured servitude and a limited form of slavery.  Taylor also had antislavery credentials since in February 1819, he had proposed a similar slave restriction for Arkansas Territory in the House, which was defeated 89–87.

Explanation:

necessary and proper clause. the congress shall have power to all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this constitution in the government of the united states, or in any department or officer thereof.

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