Show off clothes in reflection (4)

I believe the answer is:

brag

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'show off' is the definition.
(both can mean to boast about something)

'clothes in reflection' is the wordplay.
'clothes' becomes 'bra' (bra is a kind of clothes).
'in reflection' becomes 'g' (I can't justify this - if you can you should believe this answer much more).
'bra'+'g'='BRAG'

Can you help me to learn more?

(Other definitions for brag that I've seen before include "Talk boastfully" , "Boast, crow" , "game, making > boast" , "Blow one's own trumpet" , "Idle talk" .)

I've seen this clue in The Guardian.

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