Theorem termcthin

Description: A terminal category is a thin category. (Contributed by Zhi Wang, 16-Oct-2025)

	Ref	Expression
Assertion	termcthin	⊢ ( 𝐶 ∈ TermCat → 𝐶 ∈ ThinCat )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( Base ‘ 𝐶 ) = ( Base ‘ 𝐶 )
2	1	istermc	⊢ ( 𝐶 ∈ TermCat ↔ ( 𝐶 ∈ ThinCat ∧ ∃ 𝑥 ( Base ‘ 𝐶 ) = { 𝑥 } ) )
3	2	simplbi	⊢ ( 𝐶 ∈ TermCat → 𝐶 ∈ ThinCat )