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1530s, "to give (legal) confirmation to," from Latin corroboratus, past participle of corroborare "to strengthen, invigorate," from com- "together" or "thoroughly" (see com-) + roborare "to make strong," from robur, robus "strength," (see robust).
Meaning "to strengthen by evidence, to confirm" is from 1706. Sometimes in early use the word also has its literal Latin sense, especially of medicines. Related: Corroborated; corroborating; corroborative.