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Theorem bj-ablsscmn 35458
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 19400 . 2 Abel = (Grp ∩ CMnd)
2 inss2 4169 . 2 (Grp ∩ CMnd) ⊆ CMnd
31, 2eqsstri 3960 1 Abel ⊆ CMnd
Colors of variables: wff setvar class
Syntax hints:  cin 3891  wss 3892  Grpcgrp 18588  CMndccmn 19397  Abelcabl 19398
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 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-rab 3075  df-v 3433  df-in 3899  df-ss 3909  df-abl 19400
This theorem is referenced by:  bj-ablsscmnel  35459
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