Theorem idomcringd

Description: An integral domain is a commutative ring with unity. (Contributed by Thierry Arnoux, 4-May-2025) Formerly subproof of idomringd . (Proof shortened by SN, 14-May-2025)

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

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 )