Theorem crngorngo 38815

Description: Obsolete theorem, use crngringd 20412 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 38811	. 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 2145  RingOpscrngo 38709  Com2ccm2 38804  CRingOpsccring 38808

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-in 3906  df-crngo 38809

This theorem is used by:  crngm23  38817  crngm4  38818  crngohomfo  38821  isidlc  38830  dmnrngo  38872  prnc  38882  isfldidl  38883  isfldidl2  38884  ispridlc  38885  pridlc3  38888  isdmn3  38889