Theorem idomringd

Description: An integral domain is a ring. (Contributed by Thierry Arnoux, 22-Mar-2025)

	Ref	Expression
Hypothesis	idomringd.1	|- ( ph -> R e. IDomn )
Assertion	idomringd	|- ( ph -> R e. Ring )

Proof

Step	Hyp	Ref	Expression
1		idomringd.1	|- ( ph -> R e. IDomn )
2		df-idom	|- IDomn = ( CRing i^i Domn )
3	1 2	eleqtrdi	|- ( ph -> R e. ( CRing i^i Domn ) )
4	3	elin1d	|- ( ph -> R e. CRing )
5	4	crngringd	|- ( ph -> R e. Ring )