Theorem idomdomd

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

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

Proof

Step	Hyp	Ref	Expression
1		idomringd.1	⊢ ( 𝜑 → 𝑅 ∈ IDomn )
2		df-idom	⊢ IDomn = ( CRing ∩ Domn )
3	1 2	eleqtrdi	⊢ ( 𝜑 → 𝑅 ∈ ( CRing ∩ Domn ) )
4	3	elin2d	⊢ ( 𝜑 → 𝑅 ∈ Domn )