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Theorem drnggrp 17976
Description: A division ring is a group. (Contributed by NM, 8-Sep-2011.)
Assertion
Ref Expression
drnggrp  |-  ( R  e.  DivRing  ->  R  e.  Grp )

Proof of Theorem drnggrp
StepHypRef Expression
1 drngring 17975 . 2  |-  ( R  e.  DivRing  ->  R  e.  Ring )
2 ringgrp 17778 . 2  |-  ( R  e.  Ring  ->  R  e. 
Grp )
31, 2syl 17 1  |-  ( R  e.  DivRing  ->  R  e.  Grp )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1886   Grpcgrp 16662   Ringcrg 17773   DivRingcdr 17968
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-nul 4533
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-eu 2302  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-ral 2741  df-rex 2742  df-rab 2745  df-v 3046  df-sbc 3267  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-if 3881  df-sn 3968  df-pr 3970  df-op 3974  df-uni 4198  df-br 4402  df-iota 5545  df-fv 5589  df-ov 6291  df-ring 17775  df-drng 17970
This theorem is referenced by:  qqh0  28781  qqhghm  28785  dvhvaddass  34659  dvhgrp  34669  cdlemn4  34760
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