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 it can be proved from S that there is a model (V',R) of ZFC, where $V'$ is a set and R is a binary relation on $V'$ which need not be the usual $\in$ relation.

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?