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Theorem dmnrngo 26705
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 26704 . 2  |-  ( R  e.  Dmn  ->  R  e. CRingOps )
2 crngorngo 26648 . 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 1727   RingOpscrngo 21994  CRingOpsccring 26643   Dmncdmn 26695
This theorem is referenced by:  dmncan1  26724
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-iota 5447  df-fv 5491  df-crngo 26644  df-prrngo 26696  df-dmn 26697
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