In favour of really convincing evidence (5)

I believe the answer is:

proof

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

'convincing evidence' is the definition.
(I've seen this before)

'in favour of' is the wordplay.
'in favour' becomes 'pro' (I've seen this before).
'pro'+'of'='PROOF'

'really' is the link.
This may not be right. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for proof that I've seen before include "Incontrovertible evidence" , "whisky's strength?" , "Testimony" , "Decisive evidence" , "Mathematical argument" .)

I've seen this clue in the Evening Standard.

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