Metamath Proof Explorer

Theorem crngorngo

Description: Obsolete theorem, use crngringd instead. A commutative ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion crngorngo ⊢ R ∈ CRingOps → R ∈ RingOps

Proof

Step Hyp Ref Expression
1 iscrngo ⊢ R ∈ CRingOps ↔ R ∈ RingOps ∧ R ∈ Com2
2 1 simplbi ⊢ R ∈ CRingOps → R ∈ RingOps