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Metamath Proof Explorer

Theorem isdmn

Description: The predicate "is a domain". (Contributed by Jeff Madsen, 10-Jun-2010)

		Ref	Expression
	Assertion	isdmn	$⊢ R \in Dmn \leftrightarrow (R \in PrRing \land R \in Com2)$

Step	Hyp	Ref	Expression
1		df-dmn	$⊢ Dmn = PrRing \cap Com2$
2	1	elin2	$⊢ R \in Dmn \leftrightarrow (R \in PrRing \land R \in Com2)$