Metamath Proof Explorer


Theorem iscrngo

Description: The predicate "is a commutative ring". (Contributed by Jeff Madsen, 8-Jun-2010)

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 ) )