Metamath Proof Explorer

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