Theorem termcthind

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

	Ref	Expression
Hypothesis	termcthind.c	⊢ ( 𝜑 → 𝐶 ∈ TermCat )
Assertion	termcthind	⊢ ( 𝜑 → 𝐶 ∈ ThinCat )

Proof

Step	Hyp	Ref	Expression
1		termcthind.c	⊢ ( 𝜑 → 𝐶 ∈ TermCat )
2		termcthin	⊢ ( 𝐶 ∈ TermCat → 𝐶 ∈ ThinCat )
3	1 2	syl	⊢ ( 𝜑 → 𝐶 ∈ ThinCat )