I’m half a day with a Muslim leader (4)

I believe the answer is:

imam

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

'muslim leader' is the definition.
(I've seen this before)

'i'm half a day with a' is the wordplay.
'half' indicates taking half.
'a day' becomes 'mm' (I can't explain this - if you can you should give a lot more credence to this answer).
'with' means one lot of letters goes inside another.
'im' halved is 'i'.
'mm' enclosing 'a' is 'mam'.
'i'+'mam'='IMAM'

Can you help me to learn more?

(Other definitions for imam that I've seen before include "Muslim holy man" , "Prayer leader in a mosque" , "Muslim community leader" , "Accompaniment in baroque music" , "Authority on Islamic doctrine and law" .)

I've seen this clue in the Evening Standard.

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