[FOM] ZFC with Classes (ZFCC?)

[Vladik Kreinovich]

 John L. Kelley's old book General Topology has exactly such a theory. The 
original version of it is von Neumann-Bernays-Goedel VBG, Kelley had some 
changes, the theory is described in the Appendix to his book. 
 
> From: "Victor Makarov" <viktormakarov at hotmail.com>
 because ZFC is considered as "the gold standard",
> it would be very desirable to suggest also something like "ZFC with Classes 
> (ZFCC)"
> 
> - that is, a set theory with classes, as close as possible to ZFC
> (at least, more close than the other set theories with classes).
> 
> My question is:  maybe someone did it?