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Metamath Proof Explorer

Theorem iscrngo

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

		Ref	Expression
	Assertion	iscrngo	$⊢ R \in CRingOps \leftrightarrow (R \in RingOps \land R \in Com2)$

Step	Hyp	Ref	Expression
1		df-crngo	$⊢ CRingOps = RingOps \cap Com2$
2	1	elin2	$⊢ R \in CRingOps \leftrightarrow (R \in RingOps \land R \in Com2)$