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Theorem drnggrpd 39960
Description: A division ring is a group. (Contributed by SN, 16-May-2024.)
Hypothesis
Ref Expression
drngringd.1 (𝜑𝑅 ∈ DivRing)
Assertion
Ref Expression
drnggrpd (𝜑𝑅 ∈ Grp)

Proof of Theorem drnggrpd
StepHypRef Expression
1 drngringd.1 . . 3 (𝜑𝑅 ∈ DivRing)
21drngringd 39959 . 2 (𝜑𝑅 ∈ Ring)
32ringgrpd 19571 1 (𝜑𝑅 ∈ Grp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2110  Grpcgrp 18365  DivRingcdr 19767
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2708  ax-nul 5199
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2071  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3410  df-sbc 3695  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-if 4440  df-sn 4542  df-pr 4544  df-op 4548  df-uni 4820  df-br 5054  df-iota 6338  df-fv 6388  df-ov 7216  df-ring 19564  df-drng 19769
This theorem is referenced by: (None)
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