TITLE: Minimum number of axioms for ZFC set theory
QUESTION [10 upvotes]: What is the minimum number of axioms needed for ZFC Set Theory?
I have found that Suppes' Axiomatic Set Theory lists 7 axioms, but I am
not sure if this can be reduced or not.  Any references on this subject would be much appreciated.
Suppes' list:

Axiom of Extensionality
Sum Axiom
Power Set Axiom
Axiom of Regularity
Axiom of Infinity
Axiom Schema of Replacement
Axiom of Choice

REPLY [4 votes]: It seems to me the OP is asking whether any of the 7 assertions (specifically 6 axioms and a schema) listed are unnecessary, i.e. whether we can remove any one of them and still derive all of ZFC (similar to how Suppes removed pairing and comprehension because they can be proved from the other axioms). And the answer to that is no, none of these 7 assertions can be proven from the other 6. E.g., ZFC-Infinity+ $\neg$Infinity holds in the model $HF,$ and is thus relatively consistent to ZFC.