[isabelle] Should add new lemma to ZF core?

I suggest to add the following lemma similar to existing comp_eq_id_iff lemma to ZF core.
lemma comp_eq_id_iff2:
  "[| f: Af->B; g: B->Ag; Ag<=Af |] ==> f O g = id(B) <-> (ALL y:B. f`(?g`y) = y)"
I am thinking about how to prove it, but have not yet proved.
Proofs are welcomed.
So: Will we add it to ZF core or not? (Please say your options and imperatives.)
Victor Porton - http://portonvictor.org

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