The verb substantiate means to give evidence which shows something is true.
Synonyms are affirm, confirm, verify, or justify.
The word origins from Modern Latin (1650s) substantiatus, past participle of substantiare, from Latin substantia meaning “being, essence, material”. Its meaning “to demonstrate or prove” is attested from 1803.
I need to substantiate my evidence to that claim.
That photo substantiates the views of the artist.
Our suggestions must be substantiated into actions.