He could find no evidence to back up her claims.

He did not offer any evidence to back up his claim.

Not that he has any hard data to back up his claim.

Williams used data from the federal government to back up his claim.

Could you provide some statistics to back up your claim?

"Shall we see who has the power to back up their claims?"

"She's basically using my research to back up her own claim."

He called upon the newcomers to back up his claim.

You have not been able to produce witnesses to back up your claims.

But he declined to give any figures to back up his claim.