Theorem crngorngo 38935

Description: Obsolete theorem, use crngringd 20473 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 38931	. 2 ⊢ (𝑅 ∈ CRingOps ↔ (𝑅 ∈ RingOps ∧ 𝑅 ∈ Com2))
2	1	simplbi 502	1 ⊢ (𝑅 ∈ CRingOps → 𝑅 ∈ RingOps)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  RingOpscrngo 38829  Com2ccm2 38924  CRingOpsccring 38928

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-in 4091  df-crngo 38929

This theorem is used by:  crngm23  38937  crngm4  38938  crngohomfo  38941  isidlc  38950  dmnrngo  38992  prnc  39002  isfldidl  39003  isfldidl2  39004  ispridlc  39005  pridlc3  39008  isdmn3  39009