Theorem crngorngo 38679

Description: Obsolete theorem, use crngringd 20332 instead. A commutative ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
crngorngo	⊢ (𝑅 ∈ CRingOps → 𝑅 ∈ RingOps)

Proof of Theorem crngorngo

Step	Hyp	Ref	Expression
1		iscrngo 38675	. 2 ⊢ (𝑅 ∈ CRingOps ↔ (𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2))
2	1	simplbi 501	1 ⊢ (𝑅 ∈ CRingOps → 𝑅 ∈ RingOps)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2143  RingOpscrngo 38573  Com2ccm2 38668  CRingOpsccring 38672

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-in 3912  df-crngo 38673

This theorem is used by:  crngm23  38681  crngm4  38682  crngohomfo  38685  isidlc  38694  dmnrngo  38736  prnc  38746  isfldidl  38747  isfldidl2  38748  ispridlc  38749  pridlc3  38752  isdmn3  38753