Theorem crngorngo

Description: A commutative ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010)

	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 )