Literally, “are being saved.” Salvation is a continuous experience (see on Rom. 8:24; cf. COL 65).

Rather, “are holding fast,” that is, to what Paul preached unto them. This holding fast means more than a mere mental assent to the doctrines, it indicates absolute conviction of the thing believed. Such conviction would lead to behavior compatible with their faith, and would not permit them to entertain erroneous thoughts.

There was nothing wrong with the message that had been preached, but the quality of the Corinthian belief in that message may have been open to question. If their belief was halfhearted, it would have little value. If their faith was firm, then they would find Paul’s doctrine sufficient to guide them into the way of salvation. Having said that, the apostle proceeds to assure them that he had indeed given them the true gospel.