Theorem iscrngo

Description: The predicate "is a commutative ring". (Contributed by Jeff Madsen, 8-Jun-2010)

	Ref	Expression
Assertion	iscrngo	⊢ ( 𝑅 ∈ CRingOps ↔ ( 𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2 ) )

Proof

Step	Hyp	Ref	Expression
1		df-crngo	⊢ CRingOps = ( RingOps ∩ Com2 )
2	1	elin2	⊢ ( 𝑅 ∈ CRingOps ↔ ( 𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2 ) )