Metamath Proof Explorer


Theorem idomringd

Description: An integral domain is a ring. (Contributed by Thierry Arnoux, 22-Mar-2025)

Ref Expression
Hypothesis idomringd.1
|- ( ph -> R e. IDomn )
Assertion idomringd
|- ( ph -> R e. Ring )

Proof

Step Hyp Ref Expression
1 idomringd.1
 |-  ( ph -> R e. IDomn )
2 1 idomcringd
 |-  ( ph -> R e. CRing )
3 2 crngringd
 |-  ( ph -> R e. Ring )