Metamath Proof Explorer

Theorem lringring

Description: A local ring is a ring. (Contributed by Jim Kingdon, 20-Feb-2025) (Revised by SN, 23-Feb-2025)

Ref Expression
Assertion lringring 
|- ( R e. LRing -> R e. Ring )

Proof

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