Theorem thinccatd

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

	Ref	Expression
Hypothesis	thinccatd.c	$$⊢\phi \to C\in \mathrm{ThinCat}$$
Assertion	thinccatd	$$⊢\phi \to C\in \mathrm{Cat}$$

Proof

Step	Hyp	Ref	Expression
1		thinccatd.c	$$⊢\phi \to C\in \mathrm{ThinCat}$$
2		thinccat	$$⊢C\in \mathrm{ThinCat}\to C\in \mathrm{Cat}$$
3	1 2	syl	$$⊢\phi \to C\in \mathrm{Cat}$$