Theorem iscrngo

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

	Ref	Expression
Assertion	iscrngo	$$⊢R\in \mathrm{CRingOps}\leftrightarrow \left(R\in \mathrm{RingOps}\wedge R\in \mathrm{Com2}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-crngo	$$⊢\mathrm{CRingOps}=\mathrm{RingOps}\cap \mathrm{Com2}$$
2	1	elin2	$$⊢R\in \mathrm{CRingOps}\leftrightarrow \left(R\in \mathrm{RingOps}\wedge R\in \mathrm{Com2}\right)$$