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Theorem crngorngo 25773
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 25770 . 2  |-  ( R  e. CRingOps 
<->  ( R  e.  RingOps  /\  R  e.  Com2 ) )
21simplbi 446 1  |-  ( R  e. CRingOps  ->  R  e.  RingOps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1701   RingOpscrngo 21095   Com2ccm2 21130  CRingOpsccring 25768
This theorem is referenced by:  crngm23  25775  crngm4  25776  crngohomfo  25779  isidlc  25788  dmnrngo  25830  prnc  25840  isfldidl  25841  isfldidl2  25842  ispridlc  25843  pridlc3  25846  isdmn3  25847
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-in 3193  df-crngo 25769
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