The source for the date is this Royal College of Physicians page. It doesn't actually show the portrait, but it seems unlikely there are two distinct portraits. Since the artist died in 1841, the image is certainly free of copyright.
Public domain works must be out of copyright in both the United States and in the source country of the work in order to be hosted on the Commons. If the work is not a U.S. work, the file must have an additional copyright tag indicating the copyright status in the source country. Note: This tag should not be used for sound recordings.PD-1923Public domain in the United States//commons.wikimedia.org/wiki/File:Pierre_Louis_Antoine_Cordier.jpg
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