Theorem isfld

Description: A field is a commutative division ring. (Contributed by Mario Carneiro, 17-Jun-2015)

	Ref	Expression
Assertion	isfld	⊢ ( 𝑅 ∈ Field ↔ ( 𝑅 ∈ DivRing ∧ 𝑅 ∈ CRing ) )

Proof

Step	Hyp	Ref	Expression
1		df-field	⊢ Field = ( DivRing ∩ CRing )
2	1	elin2	⊢ ( 𝑅 ∈ Field ↔ ( 𝑅 ∈ DivRing ∧ 𝑅 ∈ CRing ) )