Metamath Proof Explorer

Theorem domnring

Description: A domain is a ring. (Contributed by Mario Carneiro, 28-Mar-2015)

Ref Expression
Assertion domnring 
|- ( R e. Domn -> R e. Ring )

Proof

Step Hyp Ref Expression
1 domnnzr 
 |-  ( R e. Domn -> R e. NzRing )
2 nzrring 
 |-  ( R e. NzRing -> R e. Ring )
3 1 2 syl 
 |-  ( R e. Domn -> R e. Ring )