Theorem crngorngo 39125

Description: Obsolete theorem, use crngringd 20500 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 39121	. 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 2147  RingOpscrngo 39019  Com2ccm2 39114  CRingOpsccring 39118

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-in 4094  df-crngo 39119

This theorem is used by:  crngm23  39127  crngm4  39128  crngohomfo  39131  isidlc  39140  dmnrngo  39182  prnc  39192  isfldidl  39193  isfldidl2  39194  ispridlc  39195  pridlc3  39198  isdmn3  39199