Theorem isdmn

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

	Ref	Expression
Assertion	isdmn	$$⊢R\in \mathrm{Dmn}\leftrightarrow \left(R\in \mathrm{PrRing}\wedge R\in \mathrm{Com2}\right)$$

Proof

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