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The Collaborative International Dictionary
Evidentially

Evidential \Ev`i*den"tial\, a. Relating to, or affording, evidence; indicative; especially, relating to the evidences of Christianity.
--Bp. Fleetwood. ``Evidential tracks.''
--Earle.. -- Ev`i*den"tial*ly, adv.

Wiktionary
evidentially

adv. In an evidential way; according to evidence.