Metamath Proof Explorer

Theorem dmncrng

Description: A domain is a commutative ring. (Contributed by Jeff Madsen, 6-Jan-2011)

Ref Expression
Assertion dmncrng ⊢ R ∈ Dmn → R ∈ CRingOps

Proof

Step Hyp Ref Expression
1 isdmn2 ⊢ R ∈ Dmn ↔ R ∈ PrRing ∧ R ∈ CRingOps
2 1 simprbi ⊢ R ∈ Dmn → R ∈ CRingOps