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Theorem drnggrp 15843
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 15842 . 2  |-  ( R  e.  DivRing  ->  R  e.  Ring )
2 rnggrp 15669 . 2  |-  ( R  e.  Ring  ->  R  e. 
Grp )
31, 2syl 16 1  |-  ( R  e.  DivRing  ->  R  e.  Grp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   Grpcgrp 14685   Ringcrg 15660   DivRingcdr 15835
This theorem is referenced by:  qqh0  24368  qqhghm  24372  dvhvaddass  31895  dvhgrp  31905  cdlemn4  31996
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 2417  ax-nul 4338
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-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084  df-rng 15663  df-drng 15837
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