Theorem termcnex

Description: The class of all terminal categories is a proper class. Therefore both the class of all thin categories and the class of all categories are proper classes. Note that snnex is equivalent to snglV e/ V . (Contributed by Zhi Wang, 20-Oct-2025)

	Ref	Expression
Assertion	termcnex	|- TermCat e/ _V

Proof

Step	Hyp	Ref	Expression
1		snnex	|- { b | E. x b = { x } } e/ _V
2		basrestermcfo	|- ( Base |` TermCat ) : TermCat -onto-> { b | E. x b = { x } }
3	1 2	fonex	|- TermCat e/ _V