Theorem termcbas

Description: The base of a terminal category is a singleton. (Contributed by Zhi Wang, 16-Oct-2025)

	Ref	Expression
Hypotheses	termcbas.c	|- ( ph -> C e. TermCat )
	termcbas.b	|- B = ( Base ` C )
Assertion	termcbas	|- ( ph -> E. x B = { x } )

Proof

Step	Hyp	Ref	Expression
1		termcbas.c	|- ( ph -> C e. TermCat )
2		termcbas.b	|- B = ( Base ` C )
3	2	istermc	|- ( C e. TermCat <-> ( C e. ThinCat /\ E. x B = { x } ) )
4	1 3	sylib	|- ( ph -> ( C e. ThinCat /\ E. x B = { x } ) )
5	4	simprd	|- ( ph -> E. x B = { x } )