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Theorem drnggrp 15536
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 drngrng 15535 . 2  |-  ( R  e.  DivRing  ->  R  e.  Ring )
2 rnggrp 15362 . 2  |-  ( R  e.  Ring  ->  R  e. 
Grp )
31, 2syl 15 1  |-  ( R  e.  DivRing  ->  R  e.  Grp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   Grpcgrp 14378   Ringcrg 15353   DivRingcdr 15528
This theorem is referenced by:  dvhvaddass  31909  dvhgrp  31919  cdlemn4  32010
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-nul 4165
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-rng 15356  df-drng 15530
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