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	⊢ ( 𝜑 → 𝑅 ∈ CRing )
Assertion	crngringd	⊢ ( 𝜑 → 𝑅 ∈ Ring )

Proof

Step	Hyp	Ref	Expression
1		crngringd.1	⊢ ( 𝜑 → 𝑅 ∈ CRing )
2		crngring	⊢ ( 𝑅 ∈ CRing → 𝑅 ∈ Ring )
3	1 2	syl	⊢ ( 𝜑 → 𝑅 ∈ Ring )