Suppose Morse-Kelly set theory consists of class comprehension, class foundation, class extension, axiom of infinity , limitation of size, and the general continuum hypothesis. Can the axiom of powerset,that the power set of a set is a set, be proven in this system? Without gch of course it can’t. 

If it can be proven then Morse-Kelly set theory can be presented as class comprehension, class foundation, class extension, axiom of infinity, and the following axiom which combines the axiom of limitation of size and gch: let P be the power class of a class C. If S is a class such that |S|<|P| then there exists a subclass of C with the same cardinality as S. 

Here only one axiom explicitly refers to sets, the axiom of infinity.