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Theorem bj-ablssgrp 34562
 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 18912 . 2 Abel = (Grp ∩ CMnd)
2 inss1 4208 . 2 (Grp ∩ CMnd) ⊆ Grp
31, 2eqsstri 4004 1 Abel ⊆ Grp
 Colors of variables: wff setvar class Syntax hints:   ∩ cin 3938   ⊆ wss 3939  Grpcgrp 18106  CMndccmn 18909  Abelcabl 18910 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-v 3499  df-in 3946  df-ss 3955  df-abl 18912 This theorem is referenced by:  bj-ablssgrpel  34563
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