Crossword Genius

Excellent to involve religious leader, thinking from first principles (1,6)

Ross

I believe the answer is:

a priori

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'thinking from first principles' is the definition.
Both the answer and definition are adjectives. Maybe there's a link between them I don't understand?

'excellent to involve religious leader' is the wordplay.
'excellent' becomes 'ai' (resembles 'Ap', old-fashioned term for excellent).
'to involve' is an insertion indicator (inserted letters get involved).
'religious leader' becomes 'prior' (I've seen this before).
'ai' going around 'prior' is 'A PRIORI'.

Can you help me to learn more?

(Other definitions for a priori that I've seen before include "Sort of reasoning" , "Like reasoning from cause to effect" , "Based on theoretical deduction" , "Deductive (reasoning)" , "(Reasoning) from first principles (Latin)" .)

I've seen this clue in The Independent.
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