Challenge a vain statement from me (7)

I believe the answer is:

impeach

I'm a little stuck... Click here to teach me more about this clue!

'challenge' is the definition.
(I know that impeach is a kind of challenge)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for impeach that I've seen before include "Arraign - revile" , "In America, charge with misconduct - say President" , "Criticise" , "call into question" , "Charge with a crime (against the state)" .)

I've seen this clue in The Times.

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