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Theorem bj-ablsscmn 33685
 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 18549 . 2 Abel = (Grp ∩ CMnd)
2 inss2 4058 . 2 (Grp ∩ CMnd) ⊆ CMnd
31, 2eqsstri 3860 1 Abel ⊆ CMnd
 Colors of variables: wff setvar class Syntax hints:   ∩ cin 3797   ⊆ wss 3798  Grpcgrp 17776  CMndccmn 18546  Abelcabl 18547 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-v 3416  df-in 3805  df-ss 3812  df-abl 18549 This theorem is referenced by:  bj-ablsscmnel  33686  bj-rrvecsscmn  33697
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