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Theorem drnggrp 20756
Description: A division ring is a group (closed form). (Contributed by NM, 8-Sep-2011.)
Assertion
Ref Expression
drnggrp (𝑅 ∈ DivRing → 𝑅 ∈ Grp)

Proof of Theorem drnggrp
StepHypRef Expression
1 id 22 . 2 (𝑅 ∈ DivRing → 𝑅 ∈ DivRing)
21drnggrpd 20755 1 (𝑅 ∈ DivRing → 𝑅 ∈ Grp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Grpcgrp 18964  DivRingcdr 20746
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-nul 5312
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rab 3434  df-v 3480  df-sbc 3792  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-ring 20253  df-drng 20748
This theorem is referenced by:  drgextlsp  33623  qqh0  33947  qqhghm  33951  dvhvaddass  41080  dvhgrp  41090  cdlemn4  41181  fldhmf1  42072
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