Theorem rngccatALTV

Description: The category of non-unital rings is a category. (Contributed by AV, 27-Feb-2020) (New usage is discouraged.)

	Ref	Expression
Hypothesis	rngccatALTV.c	$$⊢C=\mathrm{RngCatALTV}\left(U\right)$$
Assertion	rngccatALTV	$$⊢U\in V\to C\in \mathrm{Cat}$$

Proof

Step	Hyp	Ref	Expression
1		rngccatALTV.c	$$⊢C=\mathrm{RngCatALTV}\left(U\right)$$
2		eqid	$$⊢{\mathrm{Base}}_C={\mathrm{Base}}_C$$
3	1 2	rngccatidALTV	$$⊢U\in V\to \left(C\in \mathrm{Cat}\wedge \mathrm{Id}\left(C\right)=\left(x\in {\mathrm{Base}}_C⟼{\mathrm{I}\upharpoonright }_{{\mathrm{Base}}_x}\right)\right)$$
4	3	simpld	$$⊢U\in V\to C\in \mathrm{Cat}$$