Theorem istermc2

Description: The predicate "is a terminal category". A terminal category is a thin category with exactly one object. (Contributed by Zhi Wang, 16-Oct-2025)

	Ref	Expression
Hypothesis	istermc.b	|- B = ( Base ` C )
Assertion	istermc2	|- ( C e. TermCat <-> ( C e. ThinCat /\ E! x x e. B ) )

Proof

Step	Hyp	Ref	Expression
1		istermc.b	|- B = ( Base ` C )
2	1	istermc	|- ( C e. TermCat <-> ( C e. ThinCat /\ E. x B = { x } ) )
3		eusn	|- ( E! x x e. B <-> E. x B = { x } )
4	3	anbi2i	|- ( ( C e. ThinCat /\ E! x x e. B ) <-> ( C e. ThinCat /\ E. x B = { x } ) )
5	2 4	bitr4i	|- ( C e. TermCat <-> ( C e. ThinCat /\ E! x x e. B ) )