Theorem thinccatd

Description: A thin category is a category (deduction form). (Contributed by Zhi Wang, 24-Sep-2024)

	Ref	Expression
Hypothesis	thinccatd.c	⊢ ( 𝜑 → 𝐶 ∈ ThinCat )
Assertion	thinccatd	⊢ ( 𝜑 → 𝐶 ∈ Cat )

Proof

Step	Hyp	Ref	Expression
1		thinccatd.c	⊢ ( 𝜑 → 𝐶 ∈ ThinCat )
2		thinccat	⊢ ( 𝐶 ∈ ThinCat → 𝐶 ∈ Cat )
3	1 2	syl	⊢ ( 𝜑 → 𝐶 ∈ Cat )