Theorem drngringd

Description: A division ring is a ring. (Contributed by SN, 16-May-2024)

	Ref	Expression
Hypothesis	drngringd.1	⊢ ( 𝜑 → 𝑅 ∈ DivRing )
Assertion	drngringd	⊢ ( 𝜑 → 𝑅 ∈ Ring )

Proof

Step	Hyp	Ref	Expression
1		drngringd.1	⊢ ( 𝜑 → 𝑅 ∈ DivRing )
2		drngring	⊢ ( 𝑅 ∈ DivRing → 𝑅 ∈ Ring )
3	1 2	syl	⊢ ( 𝜑 → 𝑅 ∈ Ring )