Theorem isdmn

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

	Ref	Expression
Assertion	isdmn	⊢ ( 𝑅 ∈ Dmn ↔ ( 𝑅 ∈ PrRing ∧ 𝑅 ∈ Com2 ) )

Proof

Step	Hyp	Ref	Expression
1		df-dmn	⊢ Dmn = ( PrRing ∩ Com2 )
2	1	elin2	⊢ ( 𝑅 ∈ Dmn ↔ ( 𝑅 ∈ PrRing ∧ 𝑅 ∈ Com2 ) )