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 e. Field <-> ( R e. DivRing /\ R e. CRing ) )

Proof

Step Hyp Ref Expression
1 df-field 
 |-  Field = ( DivRing i^i CRing )
2 1 elin2 
 |-  ( R e. Field <-> ( R e. DivRing /\ R e. CRing ) )