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Theorem bj-ablsscmn 34577
Description: Abelian groups are commutative monoids. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ablsscmn Abel ⊆ CMnd

Proof of Theorem bj-ablsscmn
StepHypRef Expression
1 df-abl 18888 . 2 Abel = (Grp ∩ CMnd)
2 inss2 4184 . 2 (Grp ∩ CMnd) ⊆ CMnd
31, 2eqsstri 3980 1 Abel ⊆ CMnd
Colors of variables: wff setvar class
Syntax hints:  cin 3912  wss 3913  Grpcgrp 18082  CMndccmn 18885  Abelcabl 18886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-12 2177  ax-ext 2792
This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1540  df-ex 1781  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-rab 3134  df-v 3475  df-in 3920  df-ss 3930  df-abl 18888
This theorem is referenced by:  bj-ablsscmnel  34578
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