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Theorem crngorngo 26610
Description: A commutative ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010.)
Assertion
Ref Expression
crngorngo  |-  ( R  e. CRingOps  ->  R  e.  RingOps )

Proof of Theorem crngorngo
StepHypRef Expression
1 iscrngo 26607 . 2  |-  ( R  e. CRingOps 
<->  ( R  e.  RingOps  /\  R  e.  Com2 ) )
21simplbi 447 1  |-  ( R  e. CRingOps  ->  R  e.  RingOps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   RingOpscrngo 21963   Com2ccm2 21998  CRingOpsccring 26605
This theorem is referenced by:  crngm23  26612  crngm4  26613  crngohomfo  26616  isidlc  26625  dmnrngo  26667  prnc  26677  isfldidl  26678  isfldidl2  26679  ispridlc  26680  pridlc3  26683  isdmn3  26684
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-crngo 26606
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