This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem idomdomd

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

		Ref	Expression
	Hypothesis	idomringd.1	$⊢ φ \to R \in IDomn$
	Assertion	idomdomd	$⊢ φ \to R \in Domn$

Step	Hyp	Ref	Expression
1		idomringd.1	$⊢ φ \to R \in IDomn$
2		df-idom	$⊢ IDomn = CRing \cap Domn$
3	1 2	eleqtrdi	$⊢ φ \to R \in (CRing \cap Domn)$
4	3	elin2d	$⊢ φ \to R \in Domn$