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Theorem bj-ablssgrp 35447
Description: Abelian groups are groups. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ablssgrp Abel ⊆ Grp

Proof of Theorem bj-ablssgrp
StepHypRef Expression
1 df-abl 19389 . 2 Abel = (Grp ∩ CMnd)
2 inss1 4162 . 2 (Grp ∩ CMnd) ⊆ Grp
31, 2eqsstri 3955 1 Abel ⊆ Grp
Colors of variables: wff setvar class
Syntax hints:  cin 3886  wss 3887  Grpcgrp 18577  CMndccmn 19386  Abelcabl 19387
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-abl 19389
This theorem is referenced by:  bj-ablssgrpel  35448
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