Hello all, one may look for "minimal system of axioms" for ZFC (or any other
theory) in the following (unusual) sense : say that a subset S of ZFC is
"sufficient" if there is an explicit procedure that
constructs a model of ZFC from any model of  S.

  Thus, for example, ZF is sufficient since inside ZF we can construct Godel's
universe L which is a model for ZFC. 
   My questions : are minimal sufficient subsets of ZFC known?
Is extensionality+infinity+(abstraction scheme) sufficient?