To deliver a testimony, especially as witness(verb)
To prove, demonstrate(verb)
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Use "bear witness" in a sentence
"I am Catholic, you Protestant; but as there is but one Christ, I charge you in His name to bear witness that I die firm to my religion, a true Scotswoman and a true Frenchwoman."
"Squire Rawdon and Mrs. Rawdon testified to Dora's ill-usage; the butler, the coachman, the stablemen, the cook, the housemaids were all eager to bear witness to the same; and Mrs. Mostyn's appearance was too eloquent a plea for any humane man to deny her the mother-help she asked for."
"Such disruption of their carefully nurtured natural order would have displeased the Wais, but there were none aboard to bear witness to the persistent disturbance."