Metamath Proof Explorer

Theorem tdrgring

Description: A topological division ring is a ring. (Contributed by Mario Carneiro, 5-Oct-2015)

Ref Expression
Assertion tdrgring 
|- ( R e. TopDRing -> R e. Ring )

Proof

Step Hyp Ref Expression
1 tdrgtrg 
 |-  ( R e. TopDRing -> R e. TopRing )
2 trgring 
 |-  ( R e. TopRing -> R e. Ring )
3 1 2 syl 
 |-  ( R e. TopDRing -> R e. Ring )