Crossword Genius

One of two rugby players positioned either side of the hooker in a scrum (4)

Ross

I believe the answer is:

prop

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'one of two rugby players positioned either side of' is the definition.
I can't tell whether this defines the answer.

'hooker in a scrum' is the wordplay.
'hooker' becomes 'pro' (I've seen this before).
'in a scrum' becomes 'p' (I can't explain this - if you can you should believe this answer much more).
'pro'+'p'='PROP'

'the' is the link.

Can you help me to learn more?

(Other definitions for prop that I've seen before include "Person or thing providing support" , "Support; rugby forward" , "Object used on the set of a play" , "Temporary support" , "Stay" .)

I've seen this clue in The Times.
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