Theorem isidom

Description: An integral domain is a commutative domain. (Contributed by Mario Carneiro, 17-Jun-2015)

	Ref	Expression
Assertion	isidom	⊢ ( 𝑅 ∈ IDomn ↔ ( 𝑅 ∈ CRing ∧ 𝑅 ∈ Domn ) )

Proof

Step	Hyp	Ref	Expression
1		df-idom	⊢ IDomn = ( CRing ∩ Domn )
2	1	elin2	⊢ ( 𝑅 ∈ IDomn ↔ ( 𝑅 ∈ CRing ∧ 𝑅 ∈ Domn ) )