Description: The predicate "is a commutative ring". (Contributed by Jeff Madsen, 8-Jun-2010)
Ref | Expression | ||
---|---|---|---|
Assertion | iscrngo | ⊢ ( 𝑅 ∈ CRingOps ↔ ( 𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-crngo | ⊢ CRingOps = ( RingOps ∩ Com2 ) | |
2 | 1 | elin2 | ⊢ ( 𝑅 ∈ CRingOps ↔ ( 𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2 ) ) |