The term duly sworn refers to having been put under oath, before an officer authorized to administer oaths, in the manner and form required by law.
To "depose" is merely to state or affirm some matter of fact in an affidavit or deposition. This may be done as well before an oath is administered to the deponent as afterwards. An allegation that one did depose and swear is not the equivalent of alleging that "being duly sworn, did depose and say.". A man may depose as well before an oath has been administered to him as afterwards. Likewise a person may "swear" who is not duly sworn. [United States v. McConaughy, 33 F. 168, 169 (D. Or. 1887)].