Metamath Proof Explorer


Theorem isidom2

Description: The predicate "is an integral domain": An integral domain is a commutative prime ring. (Contributed by Jeff Madsen, 10-Jun-2010) (Revised by AV, 27-Jun-2026)

Ref Expression
Assertion isidom2 Could not format assertion : No typesetting found for |- ( R e. IDomn <-> ( R e. PrmRing /\ R e. CRing ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 dfidom2 Could not format IDomn = ( PrmRing i^i CRing ) : No typesetting found for |- IDomn = ( PrmRing i^i CRing ) with typecode |-
2 1 elin2 Could not format ( R e. IDomn <-> ( R e. PrmRing /\ R e. CRing ) ) : No typesetting found for |- ( R e. IDomn <-> ( R e. PrmRing /\ R e. CRing ) ) with typecode |-