Theorem crngringd

Description: A commutative ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010) (Revised by SN, 16-May-2024)

	Ref	Expression
Hypothesis	crngringd.1	$$⊢\phi \to R\in \mathrm{CRing}$$
Assertion	crngringd	$$⊢\phi \to R\in \mathrm{Ring}$$

Proof

Step	Hyp	Ref	Expression
1		crngringd.1	$$⊢\phi \to R\in \mathrm{CRing}$$
2		crngring	$$⊢R\in \mathrm{CRing}\to R\in \mathrm{Ring}$$
3	1 2	syl	$$⊢\phi \to R\in \mathrm{Ring}$$