Eccentric eats filth? C'est la vie! (5,4)

I believe the answer is:

thats life

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'c'est la vie' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'eccentric eats filth?' is the wordplay.
'eccentric' indicates an anagram.
'eats'+'filth'='eatsfilth'
'eatsfilth' anagrammed gives 'THATS LIFE'.

Can you help me to learn more?

(Another definition for thats life that I've seen is " Expression of the fatalist".)

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