Vagrant's religion defies logic! (7,6)

I believe the answer is:

beggars belief

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'vagrant's religion' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'defies logic' is the wordplay.
'defies' becomes 'beggars' (beggaring is a kind of defying).
'logic' becomes 'belief' (I can't justify this - if you can you should believe this answer much more).
'beggars'+'belief'='BEGGARS BELIEF'

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I've seen this clue in the Sydney Morning Herald.

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