adduce (v.)

"to bring forward, present, or offer, cite as authority or evidence," early 15c., from Latin adducere "lead to, bring to, bring along," from ad "to" (see ad-) + ducere "to lead," from PIE root *deuk- "to lead." Related: Adduced; adducing.

To allege is to make an unsupported statement regarding something; to adduce, on the other hand, is to bring forward proofs or evidence in support of some statement or proposition already made: as, he alleged that he had been robbed by A. B., but adduced no proof in support of his allegation. [Century Dictionary]