Theorem idomringd

Description: An integral domain is a ring. (Contributed by Jeff Madsen, 6-Jan-2011) (Revised by Thierry Arnoux, 22-Mar-2025)

	Ref	Expression
Hypothesis	idomringd.1	⊢ ( 𝜑 → 𝑅 ∈ IDomn )
Assertion	idomringd	⊢ ( 𝜑 → 𝑅 ∈ Ring )

Proof

Step	Hyp	Ref	Expression
1		idomringd.1	⊢ ( 𝜑 → 𝑅 ∈ IDomn )
2	1	idomcringd	⊢ ( 𝜑 → 𝑅 ∈ CRing )
3	2	crngringd	⊢ ( 𝜑 → 𝑅 ∈ Ring )