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Theorem bj-ablssgrp 35057
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 19020 . 2 Abel = (Grp ∩ CMnd)
2 inss1 4117 . 2 (Grp ∩ CMnd) ⊆ Grp
31, 2eqsstri 3909 1 Abel ⊆ Grp
Colors of variables: wff setvar class
Syntax hints:  cin 3840  wss 3841  Grpcgrp 18212  CMndccmn 19017  Abelcabl 19018
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3399  df-in 3848  df-ss 3858  df-abl 19020
This theorem is referenced by:  bj-ablssgrpel  35058
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