Jamieson, Fausset and Brown on 1 Corinthians 7:10

10. not I, but the Lord--(Compare 1Co 7:12, 25, 40). In ordinary cases he writes on inspired apostolic authority (1Co 14:37); but here on the direct authority of the Lord Himself (Mr 10:11, 12). In both cases alike the things written are inspired by the Spirit of God "but not all for all time, nor all on the primary truths of the faith" [Alford].

Let not the wife depart--literally, "be separated from." Probably the separation on either side, whether owing to the husband or to the wife, is forbidden.