Metamath Proof Explorer

Theorem iscrngo

Description: Obsolete theorem, use iscrng instead. The predicate "is a commutative ring". (Contributed by Jeff Madsen, 8-Jun-2010) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion iscrngo ⊢ R ∈ CRingOps ↔ R ∈ RingOps ∧ R ∈ Com2

Proof

Step Hyp Ref Expression
1 df-crngo ⊢ CRingOps = RingOps ∩ Com2
2 1 elin2 ⊢ R ∈ CRingOps ↔ R ∈ RingOps ∧ R ∈ Com2