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Theorem dmnrngo 26658
Description: A domain is a ring. (Contributed by Jeff Madsen, 6-Jan-2011.)
Assertion
Ref Expression
dmnrngo  |-  ( R  e.  Dmn  ->  R  e.  RingOps )

Proof of Theorem dmnrngo
StepHypRef Expression
1 dmncrng 26657 . 2  |-  ( R  e.  Dmn  ->  R  e. CRingOps )
2 crngorngo 26601 . 2  |-  ( R  e. CRingOps  ->  R  e.  RingOps )
31, 2syl 16 1  |-  ( R  e.  Dmn  ->  R  e.  RingOps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   RingOpscrngo 21955  CRingOpsccring 26596   Dmncdmn 26648
This theorem is referenced by:  dmncan1  26677
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 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-crngo 26597  df-prrngo 26649  df-dmn 26650
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